Question

If f(x)=x+4/x , g(x)= x-2, and h(x) =4x-1, what is f(h(g(x)

Answer 1

(16x² - 72x + 85) / (4x-9)

Explanation:

first put g(x) into h(x)

h(g(x)) = 4(x-2) - 1 = 4x - 8 - 1 = 4x - 9, then

f(h(g(x))) = (4x - 9) + (4/4x-9) = ((4x-9)(4x-9) + 4)/(4x-9) =

(16x² - 72x + 81 + 4)/(4x-9) = (16x² - 72x + 85)/(4x-9)

If you are missing parentheses around (x+4)/x, then the answer would be different.

Answer 2

(16x² - 72x + 85) / (4x-9)

Explanation:

first put g(x) into h(x)

h(g(x)) = 4(x-2) - 1 = 4x - 8 - 1 = 4x - 9, then

f(h(g(x))) = (4x - 9) + (4/4x-9) = ((4x-9)(4x-9) + 4)/(4x-9) =

(16x² - 72x + 81 + 4)/(4x-9) = (16x² - 72x + 85)/(4x-9)