Question

Find f(x) and g(x) such that h(x) = (f o g)(x) h(x) = (1-6x)^2 Suppose that g(x) = 1-6x f(x) = ??

A) f(x) = √(1-6x)
B) f(x) = 1-6x
C) f(x) = 1/(1-6x)
D) f(x) = (1-6x)²

Answer 1

To find f(x), we determine which function, when applied to g(x) = 1-6x, results in h(x) = (1-6x)^2. The correct function is f(x) = (1-6x)^2, matching option D.

Step-by-step explanation:

The student is asking to find the function f(x) given that h(x) = (f o g)(x) and h(x) = (1-6x)^2 with g(x) = 1-6x. To find f(x), we look for a function that, when applied to g(x), results in h(x). Because g(x) is already given as 1-6x, and h(x) is the square of that expression, namely (1-6x)^2, we can conclude that f(x) must be the operation of squaring the input. Hence, the correct choice is D) f(x) = (1-6x)^2, since when g(x) is input into f(x), it produces h(x).