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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)$$$f(x)=3 x, g(x)=x-1$$

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

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 7

Composition of Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Campbell University

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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'm gonna have to plug F of X into, uh, g of X. So that means where this extreme occurs, I'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's no number that we can'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's no restriction on the input and this is a linear function, there'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,

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