Question 176411
{{{f(x)=4-3x}}} Start with the given function.



{{{y=4-3x}}} Replace f(x) with y



{{{x=4-3y}}} Switch x and y. The goal is to solve for y



{{{x-4=-3y}}} Subtract 4 from both sides.



{{{(x-4)/(-3)=y}}} Divide both sides by -3.



{{{(-x+4)/(3)=y}}} Reduce



So the inverse function is *[Tex \LARGE f^{-1}(x)=\frac{-x+4}{3}]



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*[Tex \LARGE f^{-1}(x)=\frac{-x+4}{3}] Start with the inverse function.



*[Tex \LARGE f^{-1}(-41)=\frac{-(-41)+4}{3}] Plug in {{{x=-41}}}



*[Tex \LARGE f^{-1}(-41)=\frac{41+4}{3}] Negate -41 to get 41



*[Tex \LARGE f^{-1}(-41)=\frac{45}{3}] Add



*[Tex \LARGE f^{-1}(-41)=15] Divide



So the answer is *[Tex \LARGE f^{-1}(-41)=15]