Question

If f(x) = (1 - 3)2 for 2 > 3, then f-1(x) = ?

Answer 1

We have the following function given:

$f(x)=\text{ (x}-3)^2,\text{ x}\ge3$

And we want to find the inverse function. For this case we can do the following procedure:

First we change the x and y values in the function on this way:

$x=\text{ (y}-3)^2$

And now we just need to solve for x . We begin taking square root in both sides of the equation:

$\pm\sqrt{x}\text{ = }\sqrt{(y-3)^2}$

And simplifying we got:

$\pm\sqrt{x}=\text{ y}-3$

And finally solving for y we got:

$y=f^{-1}(x)=\sqrt{x}+3$

And the best option for this case would be the last one.