madi8747 madi8747
  • 13-09-2021
  • Mathematics
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Which function is the inverse of ſx) - 2x+ 3?

Which function is the inverse of ſx 2x 3 class=

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LammettHash
LammettHash LammettHash
  • 13-09-2021

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

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

which means

[tex]2f^{-1}(x)+3 = x[/tex]

Solve for [tex]f^{-1}(x)[/tex] :

[tex]2f^{-1}(x) + 3 = x \\\\ 2f^{-1}(x) = x - 3 \\\\ f^{-1}(x) = \dfrac{x-3}2 = \boxed{\dfrac12x-\dfrac32}[/tex]

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