Does f(x) have an inverse function? Explain your answer.
Does $f(x)$ have an inverse function? Explain your answer.
Graph of f(x)
Answer
Answer
Official answer key
No. The graph fails the horizontal line test, so $f$ is not one-one on its natural domain: for example $f(0) = f(36) = 1$.
Solving $y = x - 6\sqrt{x} + 1$ gives $\sqrt{x} = 3 \pm \sqrt{y+8}$, i.e. two values of $x$ for one $y$, so $f$ has no inverse function on $[0, \infty)$.
