Match the one-to-one functions with their inverse functions. Inverse Function f^-1(x)=4(20-x)<---> f^-1(x)=x-7<----> f^-1(x)=8(x+7)<----> f^-1(x)=-3(x-1)<---->Function f(x)=x/8-7 f(x)=x+7 f(x)=1-x/3 f(x)=20-0.25x

QUESTION POSTED AT 01/06/2020 - 03:29 PM

Answered by admin AT 01/06/2020 - 03:29 PM

The inverse of a function is obtained by making x the subject of the formular of the function.

Given the function
f(x)= \frac{x}{8} -7
the inverse of the function is obtained as follows:
y= \frac{x}{8} -7 \\  \\ y+7=\frac{x}{8} \\  \\ x=8(y+7) \\  \\ \bold{f^{-1}(x)=8(x+7)}

Given the function
[tex[f(x)=x+7[/tex]
the inverse of the function is obtained as follows:
y=x+7 \\  \\ x=y-7 \\  \\ \bold{f^{-1}(x)=x-7}

Given the function
f(x)=1- \frac{x}{3}
the inverse of the function is obtained as follows:
y=1- \frac{x}{3} \\  \\  -\frac{x}{3} =y-1 \\  \\ x=-3(y-1) \\  \\ \bold{f^{-1}(x)=-3(x-1)}

Given the function
f(x)=20-0.25x
the inverse of the function is obtained as follows:
y=20-0.25x=20- \frac{1}{4} x \\  \\ \frac{1}{4} x=20-y \\  \\ x=4(20-y) \\  \\ \bold{f^{-1}(x)=4(20-x)}
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