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?

Thanks in advance

  • 2
    $\begingroup$ Hint: $f(x)=(x-5)^2+1$. $\endgroup$ – ajotatxe Dec 8 '19 at 6:16
  • $\begingroup$ @mathmaniac. $f$ is most certainly surjective onto $[1,\infty)$. $\endgroup$ – Eric Dec 8 '19 at 6:20
  • $\begingroup$ @mathmaniac. en.wikipedia.org/wiki/Surjective_function $\endgroup$ – Eric Dec 8 '19 at 6:23
  • $\begingroup$ May be $x \mapsto \sqrt {x-1} + 5.$ $\endgroup$ – math maniac. Dec 8 '19 at 6:24
  • 1
    $\begingroup$ @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 $f^{-1}(x)=\sqrt{x-1}+5$. $\endgroup$ – Eric Dec 8 '19 at 6:34

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