What is the inverse of the function $f(x)=\frac{1}{9} x+2 ?$
$h(x)=18 x-2$
$h(x)=9 x-18$
$h(x)=9 x+18$
$h(x)=18 x+2$

Answer

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Answer

Writing this in terms of $x$ gives the inverse function of $f$ as $f^{-1}(x)=\boxed{9(x-2)}$

Steps

Step 1 ：Let's replace $f(x)$ with $y$ for simplicity, so we have $y=\frac{1}{9}x+2$

Step 2 ：In order to invert $f(x)$ we may solve this equation for $x$. That gives $y-2=\frac{1}{9}x$

Step 3 ：Multiplying both sides by 9 gives $9(y-2)=x$

Step 4 ：Writing this in terms of $x$ gives the inverse function of $f$ as $f^{-1}(x)=\boxed{9(x-2)}$