Question

Find the inverse function of f(x)= square root of 2x+2

Answer 1

The inverse function of the above function is f(x) = $\frac{x^{2} - 2}{2}$

You can find the inverse of any function by switching the f(x) and x terms. Once you have done that, solve for the new f(x). Finally, what you'll have remaining is the inverse function. The work is done for you below:

f(x) = $\sqrt{2x + 2}$ ----> Switch the x and f(x)

x = $\sqrt{2f(x) + 2}$ ---> square both sides

$x^{2}$ = 2f(x) + 2 ---> subtract 2 from both sides

$x^{2}$ - 2 = 2f(x) ----> divide both sides by 2

$\frac{x^{2} - 2}{2}$ = f(x) ----> switch the order for formatting sake.

f(x) = $\frac{x^{2} - 2}{2}$