Inverse Functions

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To find the inverse function, $f^{-1} (x)$ we follow this procedure:

replace $f (x)$ with $y$ ;
rearrange this equation to make $x$ the subject;
then replace $x$ with $f^{-1} (x)$ and $y$ with $x$ .

Examples:

f (x) = m x + c

Let $y = f (x)$ then

y = m x + c

y - c = m x

\frac{y - c}{m} = x

Replacing $x$ with $f^{-1} (x)$ and $y$ with $x$ for we get

f^{-1} (x) = \frac{x - c}{m}

f (x) = \frac{7 x + 3}{4}

y = \frac{7 x + 3}{4}

4 y = 7 x + 3

4 y - 3 = 7 x

\frac{4 y - 3}{7} = x

f^{-1} (x) = \frac{4 x - 3}{7}

from corbettmaths.com:: Inverse Functions video; Practice Questions; Textbook Exercise
Further Reading:: from mathsisfun.com; from math.net; from wikipedia.org

Notes:: The substitution of $f (x)$ with $y$ is just to make it easier to rearrange in step 2.

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