Question

find the inverse of function f(x)=1/2x+7

Answer 1

The inverse of the function is given by

$\boxed{ \: \: \displaystyle \sf{ {f}^{ - 1} (x) = \frac{1 - 7x}{2x} } \: \: }$

Given :

$\displaystyle \sf{ f(x) = \frac{1}{2x + 7} }$

To find :

The inverse of the function

Solution :

Step 1 of 2 :

Write down the given function

Here the given function is

$\displaystyle \sf{ f(x) = \frac{1}{2x + 7} }$

Step 2 of 2 :

Find inverse of the function

$\displaystyle \sf{ Let \: \: {f}^{ - 1} (x) = y}$

$\displaystyle \sf{ \implies f(y) = x}$

$\displaystyle \sf{ \implies \frac{1}{2y + 7} = x}$

$\displaystyle \sf{ \implies 2y + 7 = \frac{1}{x} }$

$\displaystyle \sf{ \implies 2y = \frac{1}{x} - 7 }$

$\displaystyle \sf{ \implies 2y = \frac{1 - 7x}{x} }$

$\displaystyle \sf{ \implies y = \frac{1 - 7x}{2x} }$

$\displaystyle \sf{ \therefore \: \: {f}^{ - 1} (x) = \frac{1 - 7x}{2x} }$

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