the-formula-cfrac59f-32-where-f-geqslant-45967-expresses-the-celsius-temperature-c-as-a-function-o-2

Name: the formula cfrac59f 32 where f geqslant 45967 expresses the celsius temperature c as a function o 2
Uploaded: 2020-03-27
Duration: 39 s
Channel: Numerade
Description: The formula $C=\frac{5}{9}(F-32),$ where $F \geqslant-459.67$ expresses the Celsius temperature $C$ as a function of the Fahrenheit temperature $F .$ Find a formula for the inverse function and interpret it. What is the domain of the inverse function?

Question

The formula $C=\frac{5}{9}(F-32),$ where $F \geqslant-459.67$ expresses the Celsius temperature $C$ as a function of the Fahrenheit temperature $F .$ Find a formula for the inverse function and interpret it. What is the domain of the inverse function?

Amrita Bhasin · Accepted Answer

this question asks us for the formula and the domain of the inverse function. We know that we would multiply by 9/5 and at 32 to both sides for the Celsius and Fahrenheit equation. Therefore we get off by itself is 9/5 C plus 32? No, we What we know is that the domain of C S F has to be greater than or equal to negative for 59.67 And the range is that it has to be greater than or equal to negative to 73.15 Therefore, the domain is negative to 73 0.15 on to infinity.

Heather Zimmers · Answer

all right, so here&#x27;s a formula that relates apparent high temperature and the Celsius temperature, and we&#x27;re going to find the inverse of it, which basically means, in this context, isolate F instead of having see isolated. And so I&#x27;m not going to switch the variables like normally, we would switch X and Y. But if I switch X if I switch C and F, then they&#x27;re no longer going to mean what we want them to mean. We don&#x27;t want to see to stand for fair and height and f to stand for Celsius, so I&#x27;m not going to switch the variables in the equation. I&#x27;m just going to isolate the other one, so I&#x27;ll start by multiplying both sides by 9/5. So 9/5 C equals F minus 32 and then add 32 to both sides. So ninth of C plus 32 equals F. So this would be what we would call the inverse then. Technically, we didn&#x27;t do any switching our inner changing of variables, but we isolated the other variable so we can interpret this as a fair in high temperature with respect to the Celsius temperature or as a function of the Celsius temperature. Now we&#x27;re interested in knowing the domain of this. Well, the domain of this function will be whatever the range of the previous function Waas. So what was the range of the previous function? If the domain was f is greater than or equal to negative 4 59.67 and we substitute that into the equation and sell for see, we end up with negative 6 26.6 Soc is greater than or equal to negative 6 26.6 That was the range of the original function, So it will be the domain of the inverse function.

Amy Jiang · Answer

okay so as to find our endless collection. So we&#x27;ll start by stopping or 30 nrf, and then we&#x27;re gonna want to solve for C. Actually, we don&#x27;t need to solve war. Um, erstwhile first theater. We just need to solve for F, which is our Fahrenheit. So we&#x27;ll start by multiplying by 9/5 on both sides. And then we have f minus very to, you know, adding 32 on both sides. We get up is equal to 9/5 C plus 2 32 So this is equal to our own wrist function. And this expresses our affair in high temperature as a function of Celsius temperature. The domain of remember interest is the range of our function, which is our Celsius function. So that means the domain of F members. Well, that&#x27;s equal. Um, that&#x27;s from negative 273 points, 15 to Infinity. And that&#x27;s including our left endpoint. And I got this number by setting, um, have to be equal to zero or sorry, I have to be equal to our minimum value, which is negative. 59 negative. 459.67 So that is, um, we&#x27;ll play that end. Have 5/9. Get a floor. 59 what? 67 Finest. Every two would attack of us. Yes, that I gives us this family right here.

Joseph Lentino · Answer

so in this problem were given the formula f equals 9/5 C plus 32 which allows us to convert from Celsius to Fahrenheit. And we have, ah, domain restriction where C is greater than or equal to negative 2 53 to 73.15 Which means I&#x27;m only looking for Celsius values from negative to 73.15 up Teoh, however hot we can ever possibly think of. Well, if we&#x27;re looking at those values well, what? Ah, fair and height values are we looking for? So substituting that value into the Fahrenheit equation, we will find out that will end up looking at all temperatures in Fahrenheit from negative for 91 point 67 Well, what does this mean? This means my original domain of my function will be the X values from negative to 73.15 to infinity and the range values will be the Y values from negative for 91.67 to infinity. Well, that will help us. And to answer some of the questions later on, the first question says, find the formula of the inverse. Okay, so the first thing that I&#x27;m going to do is solve for C. So what I&#x27;m going to do here is I&#x27;m going to subtract 32 and I&#x27;m going to multiply both sides by five nines. So 5/9 times the quantity F minus 32 is equal to see. This would be the formula for the inverse function. The second question is saying, What is the inverse function? Tell us. Well, it tells us if I&#x27;m given degrees in Fahrenheit, I can now find the that the degrees in Celsius so fair and it becomes my input. Celsius becomes my output. So given fair and height, find Celsius. And finally, we&#x27;re looking at the domain in the range of the inverse function. Well, if I go back to my domain and a range of my original function, it tells me that my domain will now be the X values. Or in this case, the better way to say that is the F values such that negative for 91.67 to infinity and my range values will be. The F valley will be the C values My output values air seized now will be the output values from negative to 73.15 to infinity. The domain in the range will then switch

Darshan Maheshwari · Answer

in this question were given that a function see which is which isn&#x27;t on self if because the cities that refuse issues and affairs of Fahrenheit. So there is a relation between see in terms of so we plug in africa and the value of C. We need to find the n words of the function that party. And we need to find that war 10 was function can be used for. So for the inverse function definitely. We need to swab the variables were given that she is equal to 5/9 F minus three to. So what we&#x27;re gonna do is uh we&#x27;re trying to isolate ethnos and we&#x27;re deploying nine. Both sides we get this are dividing by five. Both sides we got 9/5. C. Is equal to f minus 32 and adding potato. Both sides. We have a physical to 32 plus 9/5. See and this is nothing but the inverse function of uh of the above one. So this is 32 plus 9/5. 9/5. See which is nothing about uh the value of F. So this is how then those function looks like and partly asks us that what this can be used for what? So this can be used to find find the equivalent equivalent temperature in Fahrenheit when ah when when it was given and degrees issues. In other words we can convert we can convert the greasy dishes two F from this particular formula. Thank you

Ashley High · Answer

So it&#x27;s gives us the formula C equals nine over five F plus 32 to change Celsius into Fahrenheit. So we have two questions here, eh? You want to find the inverse of the formula and whether or not it&#x27;s a function. So to find the inverse, we&#x27;re switching FNC nine this a C plus 32. So we&#x27;re going to subtract 32 from both sides. F minus 32 equals nine over five C. Then to get rid of this night over five, we multiply each side by 95 over nine. Which leaves us with, I must say, negative 32 Yes, times five over nine equals. See? So that is our inverse. And yes, this is a function is a linear function, and then be we&#x27;re gonna find the degree that course the Fahrenheit temperature that corresponds to 25 degrees Celsius to Fair knight. So we&#x27;re gonna plug in 25 to see and figure out what eh? Piss. So five nights of F minus 32 equals 25 so we&#x27;re gonna multiply nine over five on both sides. These will cancel over here, so I have f minus 32 equals 45 plus 32 on both sides, so F equals 77 so 25 degrees Celsius, the same as 77 degrees Fahrenheit.

Problem

In the theory of relativity, the mass of a partic…

Problem 19 Easy Difficulty

The formula $C=\frac{5}{9}(F-32),$ where $F \geqslant-459.67$ expresses the Celsius temperature $C$ as a function of the Fahrenheit temperature $F .$ Find a formula for the inverse function and interpret it. What is the domain of the inverse function?

Answer

$F=\frac{9}{5} C+32$
$[-273.15, \infty)$

Related Courses

Biocalculus Calculus for the Life Sciences

Related Topics

Discussion

Top Calculus 1 / AB Educators

Heather Z.

Caleb E.

Kristen K.

Samuel H.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

James Stewart

Biocalculus Calculus for the Life Sciences

Heather Z.

Caleb E.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$F=\frac{9}{5} C+32$$[-273.15, \infty)$

Biocalculus Calculus for the Life Sciences

Heather Z.

Caleb E.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Heather Z.

Caleb E.

Kristen K.

Samuel H.

$F=\frac{9}{5} C+32$
$[-273.15, \infty)$

James Stewart

Biocalculus Calculus for the Life Sciences