Question

Let f(x)= x^2+1. Find and simplify the following:

(a) f(x-4)=
(b) f(x-4)-f(-4)

Answer 1

f(x-4) = x²-8x + 17

f(x-4)-f(-4) = x²-8x

Explanation:

Given the function:

f(x) = x^2+1

f(x-4) = (x-4)^2+1

f(x-4 ) = x² - 8x + 16 + 1

f(x-4) = x²-8x + 17

For f(x-4)-f(-4)

f(-4) = (-4)²+1

f(-4) = 16+1

f(-4) = 17

f(x-4)-f(-4) = x²-8x + 17 - 17

f(x-4)-f(-4) = x²-8x