Answer:
[tex]f^{-1}(x) = \frac{\sqrt{x}}{13}[/tex]
Step-by-step 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:
[tex]f(x) = 169x^2[/tex]
That is:
[tex]y = 169x^2[/tex]
Exchanging x and y:
[tex]x = 169y^2[/tex]
Isolating y:
[tex]y^2 = \frac{x}{169}[/tex]
[tex]y = \sqrt{\frac{x}{169}}[/tex]
[tex]y = \frac{\sqrt{x}}{13}[/tex]
[tex]f^{-1}(x) = \frac{\sqrt{x}}{13}[/tex]
