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. g (f[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 value of the composite function G of F. Of H. Of negative three. Let's take a look at G of F. Of H. Of negative three and figure out where do we start? Well, we always start with the innermost function of a composite function. So in this case that's going to be a church of -3. Each of X was X squared plus two X plus six. So for H of negative three we are going to substitute a negative three anywhere. There was an X in R. H. Of X function. So instead of X squared it's negative three squared plus two times not X. But now two times negative three plus six. And simplifying this negative three squared is positive nine, two times negative three is negative six. And then plus six. Well the negative six plus six that is zero. So we've just got nine for our H of negative three. Alright, what's next in our composite function Now we need to put our age of negative three. Inside of our f function. R F of X is three X minus eight. So for F of H of negative three, that will be our H of negative three value inside the F of X function wherever there's an X. So H of negative three equals nine. That means we're going to put a nine in anywhere. There's an X in R. F. Of X function. So not three times X but three times nine -83 times nine is 27 -8. 27 -8 is 19. All right. What's next? We're going to put our F. Of H of negative three inside of our G function. R. G of X equals five X minus four. So for G. Of let me give a little more room for our G. Of F. Of H. Of negative three. We're going to put F. Of H of negative three in wherever there was an X in R. G. Of X function and our F of H of negative three is 19. So for G of X no longer five times X but now five times 19 minus four. And our five times 19 is 95 minus four. So 95 minus four is 91. R G f F of H of negative three is 91. We look at our answer choices and that matches with answer choice. B. Well done. We'll catch you on the next one

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. g (f[h (1)])

Key Concepts

Function Composition

Evaluating Functions

Linear vs. Quadratic Functions

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