Answer to Question #172364 in Algebra for william

Question

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Solve for the inverse y= square root of x-2+4

Answer 1

Given the function

$$y =\sqrt{x-2}+4\\$$

Let

$$y=f(x)$$

$$\therefore f(x) =\sqrt{x-2}+4\\$$

We want to find $f^{-1}(x)$

$$y =\sqrt{x-2}+4\\ y-4 =\sqrt{x-2}\\$$

Squaring both sides

$$(y-4)^2 =(\sqrt{x-2})^2\\ (y-4)^2 = x-2\\ (y-4)^2+2 = x$$

Therefore, the inverse of the function is

$$f^{-1}(x) = (x-4)^2+2$$