in-11-18-a-find-hx-when-hxgfx-b-what-is-the-domain-of-hx-c-what-is-the-range-of-mathrmhx-d-graph-m-2

Question

In $11-18 :$ a. Find $h(x)$ when $h(x)=g(f(x)) .$ b. What is the domain of $h(x) ?$ c. What is the range of $\mathrm{h}(x) ?$ d. Graph $\mathrm{h}(x)$
$$
f(x)=3 x, g(x)=x-1
$$

Finian Lickona · Accepted Answer

all right. So forthis exercise, we have to find h of X, which is equal to G of f of X, where g of X equals X minus one and f of X equals three x. So in order to find G h of X, I&#x27;m gonna have to plug F of X into, uh, g of X. So that means where this extreme occurs, I&#x27;m gonna plug him whatever f of X is so that means that g of f of X equals three X minus one. So h of X equals three X minus one. Now we need to find the domain of H of X. Now there&#x27;s no number that we can&#x27;t plug in for X to. The domain is all rials, and we need to find the range of H of X and again. Since there&#x27;s no restriction on the input and this is a linear function, there&#x27;s no restriction on the output, So the range is also going to be all rials and now we need to sketch the graph of h of X or Y. Intercept is negative one and our slope is positive. Three. Some things we go over one up. One, 23 If we connect those two, we get something that looks like this. Okay,

Finian Lickona · Answer

Okay, So for this exercise, we have a chav ex defined as G of f X and were given that f of X equals three X minus one and G of X equals 1/3 quantity X plus one. So in order, fi h of X, I&#x27;m going evaluate what happens when I plug F of X into G effects. So G on f of X equals 1/3 times and then we have an X ray here, so we&#x27;re gonna plug in three X minus one for that X quantity plus one. Now, if I simplify this thes this negative one in this positive one, cancel each other out. And I&#x27;m love with 1/3 of three eggs, which just equals X So h of X is just actually X. So the domain of H of X is all real numbers because we have no restriction on the inputs we can choose. And because the domain is all real numbers and it&#x27;s a Lanier function, we can say that the range is also all real numbers because there&#x27;s no restriction on the possible outputs we could have, because our outputs are actually always going to be identical to our input. Okay. And finally, for the graph of h of X is literally just the probably the simplest scrap of all. Just y equals X. Ah, linear wonder one function. Every input is identical to every output. So positive to returns positive to negative to returns. Negative too. And, yeah.

Finian Lickona · Answer

So for this exercise, we need to find a chav X to find his G of f of X, where FX is equal to the absolute value of two plus X and G of X is equal to negative X. So I&#x27;m gonna start by plugging F of X into G of x o g f of X equals negative. And then what goes in here? The two plus X, perhaps a value to plus sex. So we have to find the domain and there&#x27;s no restriction on any of the X values we can choose. The domain is all rials, and we&#x27;ll notice for the range, which is all the possible output values, that there&#x27;s no X value we can pick that will make this function evaluate to a positive number. If we were to pick negative to, that would be two plus negative too, which is zero. If we were to pick, uh, negative three. We have to close a negative three, which is negative. One absolute value of negative one is one, but then negated. It&#x27;s negative one again. So our range is actually all why values less than or equal to zero and the graph of this function looks something like this. You&#x27;ll see if we plug in negative too. We get zero. If we plug in zero, we get negative too. And if we plug in negative four, we get to minus negative for negative to absolute value of negative to positive. To negated is also negative too. So that&#x27;s the graph of dysfunction right here, which we&#x27;ve defined as H of X.

Finian Lickona · Answer

Okay, So for this exercise, we need to find a church of X, which is defined as G of f of X, where f of X equals for plus X on G of X equals X squared. So that means I need to plug this f of X term into G of X. Wherever the ex term occurs. Some things that G of f of X equals four plus X squared. If we expend that out, we get X squared was eight x plus 16. And now we need to find the domain of H of X. And there&#x27;s no restriction on the inputs. So our domain is going to be all really values. And now we need to find the range of H of X, which, um, if you ah, look at this. You&#x27;ll see that there is no way that we can generate a negative output because if we plug and say negative one, we get one minus a plus 16 which is a positive value. If we plug in negative too, we get four minus 16 plus 16 which is also a positive value. So there&#x27;s really no way to get any negative values, So our ranges all values of why greater than or equal to zero. And for our last portion of the assignment, we have to graft dysfunction. I&#x27;ve already generated the graph just for convenience. It&#x27;s very easy to see how you would generate the graph. Since this is just ah, linear shift of the graph of X squared, we know that we just have to find the one X intercept, which is obviously going to be negative for because four plus negative for a zero. So that&#x27;s going to make our Y output zero. And then from there it&#x27;s just a matter of graphing the, uh, standard X squared.

Suman Saurav Thakur · Answer

we have thought a number five in vintage apart is question Find at Joe from minus two. Find out of minus two edge of zero edge of two and out of three. That&#x27;s off minus door. So this is minus one. This is minus two. So that f minus two will be zero and one so minus two. Come on. So the city just minus two. That&#x27;s a minus. Dewey&#x27;s one. No, at Joe&#x27;s. Zito that the value of this function objects at zero. So at X equal to zero. That is a reason this is minor Soufun. So this is minus one. We have so find at two as do this one. This is two. This is three so as to equal to three at three called Oh, this is Trieste. Recall toe four. So these are dancers for part A. Now we have part B. Find the domain in range of it dominated all the values off X for which the graph is present. So domain is from minus 3 to 4. Okay, arrange will be France will be from here to this minus one. So Anjali minus went to for minus 12 For this is the range. Now comes part c. Find a valid attacks for which at X equal to three We haven&#x27;t provided at Jack&#x27;s equal to three. So we have to find out X equal to three for with Celebrex. So three is for X equal to two for X equal to do. Okay, it&#x27;s a part day. Find the values of X for which at checks less than equal to three. So checks will be less than equal to three. So we should find the values off X business three. So values affects for which the graph is here. So we will be having minus 3 to 2 for ex belongs to minus three to So these are the answers. Thank you so much.

Dale Sanford · Answer

Let&#x27;s find the domain of our function H of X equals three x plus six. So to find the domain, we have to look for any problems that would cause this function to not exist. That is, Are there any values that would make us divide by zero or take the square root of a negative number? In this case, no. No matter what you plug in to this function, you&#x27;ll end up with a whole number because it is a linear function. Therefore, the domain for this is just the real numbers that is the set from negative infinity to positive infinity every single number that you can think of now something different is going to be our next function. F of X equals one over X minus four. With this function, there is a problem because if the denominator x minus four equals zero, then the function will cease to exist. So we can&#x27;t let that happen. What would cause the denominated equal to zero? Well, solving this equation for X gives X equals four. Thus, X equals four is not allowed in the domain because it would cause this denominator two equals zero, which is not allowed Therefore, the domain for this function is the set of all real numbers. Besides four that is negative. Infinity all the way up to four, not inclusive, that is, using this round bracket to show that it&#x27;s not included and then four all the way to positive infinity. So this is our domain of our function. Every single rial number except for four.

Problem

In $11-18 :$ a. Find $h(x)$ when $h(x)=g(f(x)) .$…

Problem 12 Hard Difficulty

In $11-18 :$ a. Find $h(x)$ when $h(x)=g(f(x)) .$ b. What is the domain of $h(x) ?$ c. What is the range of $\mathrm{h}(x) ?$ d. Graph $\mathrm{h}(x)$
$$
f(x)=3 x, g(x)=x-1
$$

Answer

a) $h(x)=3 x-1$
b) $\mathbb{R}$
c) $\mathbb{R}$
d) See graph

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Ann Xavier Gantert

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Absolute Value - Example 1

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a) $h(x)=3 x-1$b) $\mathbb{R}$c) $\mathbb{R}$d) See graph

Algebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Maria G.

Michael J.

a) $h(x)=3 x-1$
b) $\mathbb{R}$
c) $\mathbb{R}$
d) See graph

Ann Xavier Gantert

Algebra 2 and Trigonometry