In Exercises 59-64, let
f(x) = 2x - 5
g(x) = 4x - 1
h(x) = x² + ...

Question

In Exercises 59-64, let
f(x) = 2x - 5 
g(x) = 4x - 1
h(x) = x² + x + 2.
Evaluate the indicated function without finding an equation for the function. f(g[h (1)])

Accepted Answer

Welcome back. I'm so glad you're here. We have three functions. We have F. Of X equals three X minus eight. We have G of x equals five X minus four. And we have a choice of X equals X squared plus two. X plus six. And we are to find the composite function F of G. Of H. Of one. Alright so let's look at F. Of G of H. Of one and think about what are we doing first? We start with the very innermost function which here is H. Of one. We recall that H. Of X was X squared plus two. X plus six. So H. Of one is where we'll substitute a one in for any X value that we saw in our H. Of X. So X squared is now going to be a one squared plus two times not X. But one plus six. And we do the simplification, one squared is one plus two times one is two plus six. Well one plus two plus six equals nine. So H. Of one equals nine. Great. Okay what's the next thing we're going to take a look at for our F. Of G of H. Of one? Well the H. Of one now goes inside the G function. The G of X was five X -4. So when we have g. of h. of one we're going to substitute R. H. Of one wherever we had an X. In R. G of X function in R. H. Of one equals nine. So we're going to substitute A nine wherever there's an X. And our G of X function. So it's not five exits five times nine -45 times nine is 45 -4 and 45 -4 is 41. So g. of h. of one is 41. Now what's left? Just R. F. Of X. So we recall that our f. of x function is three X -8. And for F. Of G. Of H. Of one, we're going to substitute our G. Of H. Of one in anywhere there was an X. In R. F. Of X. Function and our G. Of H. Of one is 41. So we're going to substitute 41 for X. And F. Of X. Function so not three X. But now it's three times 41. That one looks like the parentheses. So 41 minus eight three times 41 is 100 and 23 minus eight and 123 minus eight is 115. And that's exactly what we're looking for. 115 we look at our answer choices and this matches with answer choice. D. Well done. We'll catch you on the next one

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In Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. f(g[h (1)])