In Exercises 93-94, let f(x) = x² − x + 4 and g(x) = 3x – 5. Find...

Question

In Exercises 93-94, let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g (1) and f(g(1)).

Accepted Answer

Welcome back. I'm so glad you're here. We have two functions. We've got F. Of X equals to X to the one third minus X plus four. And we've got G. Of X equals X plus 19. Were to solve for two different things here were to solve for G. Of eight and we're to solve for F. Of G. Of eight. So let's work on G. Of eight first. So looking at our G. Of X. Well right underneath that G. Of eight because anywhere there was an X. In our original G. Of X equation, we're now going to replace that with an eight. So instead of X plus 19 it's eight plus 19. So G of eight equals eight plus 19, which is 27. Alright now looking back at our F. Of X, we want to solve for F. Of G. Of eight. Well we know that G of eight is 27. So we're solving for F. Of 27 meaning that anywhere there was an X. In R. F. Of X. Equation, we're now going to replace it with A. 27. So it's now two times not X. But two times 27 raised to the one third minus not X. But 27. And plus four K. Starting with our exponents 27 to the one third, that's the cubed root of 27. And that's three. So we've got two times three minus plus four, two times +36. So we've got six minus 27 plus four and six minus 27 plus four is negative 17. We look at our answer choices and that matches with answer choice B. Well done, we'll catch you on the next one.

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