Question

Can you help me answer number 21 please?

Answer 1

Option B,
`n(x)=81x^3`

Explanation:

Given:

m(x)=2√x

m(n(x))=18√x^3

To find the expression for n(x), we need to determine the relationship between m(x) and n(x) from the given information.

Substitute m(x) into the equation m(n(x))=18√x^3 and solve for n(x).

`2√(n(x))= 18√(x^3) \\\\\\\Longrightarrow √(n(x))= 9√(x^3)\\\\\\\Longrightarrow (√(n(x)))^2= (9√(x^3))^2\\\\\\\therefore \boxed{\boxed{n(x)=81x^3}}`

Thus, option B is correct.