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-7

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 $\mathrm{h}(x)$
$$
\mathrm{f}(x)=5-x, \mathrm{g}(x)=|x|
$$

Finian Lickona · Accepted 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.

Finian Lickona · 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.

Charles Carter · Answer

gives effort backs and g of X. So we have of X is equal to two x squared minus 18 and were given g of X as negative three X minus seven part. I just want you to find the domain. And since the domain about these functions, it&#x27;s all real numbers. Ever performing addition. It was the domain of the addition of these two functions. That&#x27;s gonna be the intersection of the real numbers and the real numbers, as the domain is just all real numbers. And that&#x27;s just because it&#x27;s addition. And both these functions have no domain issues. Okay, so part B do down here wants me to find h of five, or h is f of next plus G of X. So 85 was gonna plug in five everywhere we see ex around, two times five square, minus 18 course. Negative. Three times five minus seven. Okay, five squared is 25 times two is 50 15 minus 18. Negative. Three times five is negative. 15. You know, minus seven. Okay, uh, because we can come out of our all of our negatives. So negative 18 minus 15 is third. Negative. 33 maybe 33 minus seven. Negative. 40. So it&#x27;s gonna 15 minus 40 which is just equal to 10. Okay, thank you very much.

Problem

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

Problem 17 Easy 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 $\mathrm{h}(x)$
$$
\mathrm{f}(x)=5-x, \mathrm{g}(x)=|x|
$$

Answer

a) $h(x)=|5-x|$
b) $\mathbb{R}$
c) $\mathbb{R}^{+}$
d) See graph

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a) $h(x)=|5-x|$b) $\mathbb{R}$c) $\mathbb{R}^{+}$d) See graph

Algebra 2 and Trigonometry

Catherine R.

Heather Z.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Heather Z.

Caleb E.

Kristen K.

a) $h(x)=|5-x|$
b) $\mathbb{R}$
c) $\mathbb{R}^{+}$
d) See graph

Ann Xavier Gantert

Algebra 2 and Trigonometry