Find (gOf) (x)

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

g (x) = 8x-2

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

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