Respuesta :
Answers:
[tex]f^{-1}(x) = \frac{x-b}{m}\\\\[/tex]
and
[tex]h^{-1}(x) = \frac{x+9}{2}\\\\[/tex]
See note below
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Explanation:
First we replace f(x) with y. Then we swap x and y. Afterward, solve for y to determine the inverse function. The m value cannot be zero to avoid dividing by zero.
[tex]f(x) = mx+b\\\\y = mx+b\\\\x = my+b\\\\x-b = my\\\\y = \frac{x-b}{m}\\\\f^{-1}(x) = \frac{x-b}{m}\\\\[/tex]
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For the formula h(x) = 2x-9, we see that m = 2 and b = -9
So the inverse for h(x) would be:
[tex]h^{-1}(x) = \frac{x-b}{m}\\\\h^{-1}(x) = \frac{x-(-9)}{2}\\\\h^{-1}(x) = \frac{x+9}{2}\\\\[/tex]
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Note: The function [tex]h^{-1}(x) = \frac{x+9}{2}\\\\[/tex] is the same as saying [tex]h^{-1}(x) = \frac{1}{2}x+\frac{9}{2}\\\\[/tex] or [tex]h^{-1}(x) = 0.5x+4.5\\\\[/tex], so it will depend on what format your teacher wants.
