Question

Find (gOf)(x)

f(x)=x^2-(1/2x)+4
g(x)=8x-2

Answer 1

f(x)=x^2-(1/2)x+4
g(x)=8x-2
(g o f)(x)=?

(g o f)(x)=g(f(x))=g(x^2-(1/2)x+4)
x=x^2-(1/2)x+4→g(x^2-(1/2)x+4)=8[x^2-(1/2)x+4]-2
g(x^2-(1/2)x+4)=8x^2-4x+32-2
g(x^2-(1/2)x+4)=8x^2-4x+30

Answer: (g o f)(x)=8x^2-4x+30

Answer 2

For this case, the first thing we must do is the composition of functions.
We have:
f (x) = x ^ 2- (1 / 2x) +4
g (x) = 8x-2
(gOf) (x) = 8 (x ^ 2- (1 / 2x) +4) -2
We rewrite: now the function:
(gOf) (x) = 8x ^ 2- (8/2) x + 32-2
(gOf) (x) = 8x ^ 2-4x + 30
Answer:
The final result is:
(gOf) (x) = 8x ^ 2-4x + 30