Find the inverse of each function. Is the inverse a function?

Please help me with this problem?

Question

Find the inverse of each function. Is the inverse a function?

Please help me with this problem?

anonymous · Answer

@jim_thompson5910  can you explain this to me?

jim_thompson5910 · Answer

To find the inverse, swap x and y, then solve for y

$$\Large y = x^2 + 2$$

$$\Large x = y^2 + 2$$

$$\Large x-2 = y^2$$

$$\Large y^2 = x-2$$

$$\Large y = \pm\sqrt{x-2}$$

$$\Large f^{-1}(x) = \pm\sqrt{x-2}$$


Because y is effectively two functions at the same time (plus/minus of $\Large \sqrt{x-2}$), there is no way y can be a single function. Also, graphing this function will show us that it fails the horizontal line test. So the inverse is NOT a function.