# Inverse Image function

Let $$A= [{5}, \infty[$$ , $$B=[{1}, \infty[$$ and $$f: A \to B, f(x)=x^2-{10}x+{26}$$

Determine the inverse image $$f^{-1}:\ B \to A, f^{-1}(x)$$

How should I proceed with this?

• Hint: $f(x)=(x-5)^2+1$. – ajotatxe Dec 8 '19 at 6:16
• @mathmaniac. $f$ is most certainly surjective onto $[1,\infty)$. – Eric Dec 8 '19 at 6:20
• May be $x \mapsto \sqrt {x-1} + 5.$ – math maniac. Dec 8 '19 at 6:24
• @Emilycodes you mean to ask for the inverse function, not the inverse image; see math.stackexchange.com/questions/3286150/…. The inverse image/preimage of your function is $f^{-1}(B)=[5,\infty)$, the inverse function, given that $f$ is one-to-one on its domain, is $f^{-1}(x)=\sqrt{x-1}+5$. – Eric Dec 8 '19 at 6:34