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

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

f(x-4) = x²-8x + 17

f(x-4)-f(-4) = x²-8x

Step-by-step 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

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

the answer is 31.27mph