Question

Given the following: f(x) = 3x - 7; g(x) = 13x - 2; and h(x) = 6xh(h(g(x))) equals 39x - 13.TrueFalse

Answer 1

Answer: False.

Explanation

As we are asked to find h(h(g(x))), then, we have to replace all the x in h(x) over the function g(x), and then replace this expression in h(x). Thus, to solve this we can find first h(g(x)):

$h(g\mleft(x\mright))=6(13x-2)$

Simplifying:

$h(g(x))=78x-12$

Next, we have to replace this expression in h(x):

$h\mleft(h(g(x)\mright)=6(78x-12)$$h\mleft(h(g(x)\mright)=468x-72$

As 468x – 72 ≠ 39x - 13, then it is false.