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Find the inverse of the function on the given domain. f(x)=(x−6)^2, [6,∞)

Sagot :

To find the inverse function to the given one, we have to solve the expression for x:

[tex]\begin{gathered} f(x)=(x-6)^2 \\ \sqrt{f(x)}=x-6 \\ \sqrt{f(x)}+6=x \end{gathered}[/tex]

Now, change f(x) for x and x for f^-1(x) to obtain the inverse function:

[tex]f^{-1}(x)=\sqrt{x}+6[/tex]

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