Question

Write a rule for $g(x)=-f(2x)+1$ when $f(x)=$ $\frac{1}{2}$
$x^5+x^3-4x-4$ .

Answer 1

First compute f(2x):
f(2x) = (1/2)(2x)^5 + (2x)^3 - 4(2x) - 4
= (1/2)(32x^5) + 8x^3 - 8x - 4
= 16x^5 + 8x^3 - 8x - 4.

Then g(x) = -f(2x) + 1 = -(16x^5 + 8x^3 - 8x - 4) + 1
= -16x^5 - 8x^3 + 8x + 5.