Question

If f(x) = 1/2x + 4 and g(x) = -8f(x), what equation shows the correct rule for the function g?

a) g(x) = -8x - 32
b) g(x) = -4x + 4
c) g(x) = -4x - 32
d) g(x) = -4x

Answer 1

The correct rule for the function g(x), when f(x) = 1/2x + 4 and g(x) = -8f(x), is g(x) = -4x - 32, which corresponds to answer choice (c).

Step-by-step explanation:

A student asked, "If f(x) = 1/2x + 4 and g(x) = -8f(x), what equation shows the correct rule for the function g?". To find the function for g(x), we need to multiply the entire function f(x) by -8:

g(x) = -8(1/2x + 4)

Distributing the -8, we get:

g(x) = -8(1/2)x - 8(4)

g(x) = -4x - 32

So the correct equation for the function g is:

g(x) = -4x - 32

Therefore, the correct answer is (c) g(x) = -4x - 32.