Question

Given: f(x) = x - 7 and h(x) = 2x 3write the rule for f(h(x)).

a) f(h(x)) = 2x - 7
b) f(h(x)) = 2x - 4
c) f(h(x)) = 3x - 4
d) f(h(x)) = 3x - 7

Answer 1

The correct rule for f(h(x)) is d) f(h(x)) = 3x - 7.

Step-by-step explanation:

To find f(h(x)), you substitute the function h(x) = 2x³ into the function f(x) = x - 7. This means that wherever x appears in f(x), it will be replaced by h(x), which is 2x³.

Therefore, f(h(x)) = f(2x³). Now, substitute 2x³ into f(x) = x - 7. So, f(h(x)) = 2x³ - 7 = 3x - 7.

This process derives the expression f(h(x)) = 3x - 7, making option d) the correct answer among the choices provided. OPTION D