Question

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

Answer 1

Answer:

-27648

Step-by-step 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 :)