Question

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



Please help me with this problem?

Answer 1

@jim_thompson5910 can you explain this to me?

Answer 2

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.