Question

What is the inverse of the function f(x) = 169x2 when x ≥ 0?

A- f−1(x) = 13‾‾
B- f−1(x) = √13
C- f−1(x) = 13x
D- f−1(x) = 113

Answer 1

`f^(-1)(x) = (√(x))/(13)`

Explanation:

Inverse function:

Suppose we have a function y = f(x). To find the inverse, we exchange the y and the x values, and then isolate y.

Function:

`f(x) = 169x^2`

That is:

`y = 169x^2`

Exchanging x and y:

`x = 169y^2`

Isolating y:

`y^2 = (x)/(169)`

`y = \sqrt{(x)/(169)}`

`y = (√(x))/(13)`

`f^(-1)(x) = (√(x))/(13)`