Question 156161
Is the function {{{f(x)=(1/2)x}}} ?



{{{f(x)=(1/2)x}}} Start with the given expression



{{{y=(1/2)x}}} Replace {{{f(x)}}} with "y"



{{{x=(1/2)y}}} Switch "x" and "y"



{{{2x=y}}} Multiply both sides by 2 to solve for "y"



So after solving for "y", we get {{{y=2x}}}. So the inverse function is *[Tex \LARGE f^{-1}\left(x\right)=2x]



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Or...


Is the function {{{f(x)=(1)/(2x)}}} ?



{{{f(x)=(1)/(2x)}}} Start with the given expression



{{{y=(1)/(2x)}}} Replace {{{f(x)}}} with "y"



{{{x=(1)/(2y)}}} Switch "x" and "y"



{{{2xy=1}}} Multiply both sides by {{{2y}}} 



{{{y=1/(2x)}}} Divide both sides by {{{2x}}} to solve for "y"



So after solving for "y", we get {{{y=1/(2x)}}}. So the inverse function is *[Tex \LARGE f^{-1}\left(x\right)=\frac{1}{2x}]