Question

Given the functions f(x) = x ^ 3, g(x) = 9 and h(x) = 2x , what is an expression equivalant to f(2x) + 3g(x)/h(x) + 3?

Answer 1

an expression equivalent to f(2x) +
`3(g(x))/(h(x))` + 3 = 8x³ +
`(27)/(2)x` + 3

Explanation:

As given ,

f(x) = x³ , g(x) = 9 , h(x) = 2x

Now,

f(2x) = (2x)³ = 2³.x³ = 8x³

⇒f(2x) = 8x³

Now,

`(g(x))/(h(x)) = (9)/(2x) = (9)/(2)x`

⇒
`3(g(x))/(h(x)) = 3.(9)/(2)x = (27)/(2)x`

∴ we get

f(2x) +
`3(g(x))/(h(x))` + 3 = 8x³ +
`(27)/(2)x` + 3