Question

F(x) = 9x², x ≥ 0 find the inverse

Answer 1

The inverse of the function f(x) = 9x^2 is f^-1(x) = sqrt(x/9). To obtain the inverse, replace f(x) with y, solve for x in terms of y, and replace x with f^-1(x).

Explanation:

To find the inverse of the function f(x) = 9x^2, we can follow these steps:

1. Replace f(x) with y: y = 9x^2
2. Solve for x in terms of y:

y = 9x^2

y/9 = x^2

±sqrt(y/9) = x

Note that we include both positive and negative square roots, but since x ≥ 0 in the domain of the original function, we only take the positive square root.

3.Replace x with f^-1(x):

f^-1(x) = sqrt(x/9)

Therefore, the inverse of the function f(x) = 9x^2 is f^-1(x) = sqrt(x/9).

Answer 2

y = √x/3 or -√x/3

Explanation:

f(x) = 9x^2

y = 9x^2

x = 9y^2

`\sqrt{(x)/(9) }` = y

y = √x/3 or -√x/3