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If f(x) = 2x + 10, then f^-1(x) =

Sagot :

LammettHash

If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then

[tex]f\left(f^{-1}(x)\right) = x[/tex]

by definition of inverse function. We have

[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 10 = x[/tex]

Solve for the inverse :

[tex]2f^{-1}(x) + 10 = x \\\\ 2f^{-1}(x) = x-10 \\\\ \boxed{f^{-1}(x) = \dfrac{x-10}2}[/tex]

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