Question

If f(x)=x^2−8x and g(x)=−12x^2 what is g(f(−4))?

Answer 1

-27648

Explanation:

In this problem, we are looking for the function of g in terms of the function f. Simply put, we just replace the variable x in the function g with f(-4).

Step 1, writing g(f(-4)):

`g(f(-4))=-12(f(x))^2`

Great! Let us substitute f(x) with the given expression.

Step 2, substituting and simplifying:

`\\g(f(-4))=-12(x^2-8x)^2\\g(f(-4))=-12((-4)^2-8*(-4))^2\\g(f(-4))=-12(16+32)^2\\g(f(-4))=-12*2304\\g(f(-4))=-27648`

g(f(-4) is
`\fbox{-27648}`.

I hope this helps! Let me know if you have any questions :)