The inverse function of the above function is f(x) = [tex] \frac{x^{2} - 2}{2} [/tex]
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) = [tex] \sqrt{2x + 2} [/tex] ----> Switch the x and f(x)
x = [tex] \sqrt{2f(x) + 2} [/tex] ---> square both sides
[tex] x^{2} [/tex] = 2f(x) + 2 ---> subtract 2 from both sides
[tex] x^{2} [/tex] - 2 = 2f(x) ----> divide both sides by 2
[tex] \frac{x^{2} - 2}{2} [/tex] = f(x) ----> switch the order for formatting sake.
f(x) = [tex] \frac{x^{2} - 2}{2} [/tex]
