How do you find the inverse of $f(x)=(2-3x)/4$ ?

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Answer 1 · 2015-12-19T13:45:54

$bar(f(x)) = (2-4x)/3$

If $bar(f(x))$ is the inverse of $f(x)$
then, by definition of inverse, $f(bar(f(x))) = x$

Therefore
$f(bar(f(x))) = (2-3(bar(f(x))))/4 = x$

$2-3(bar(f(x)))=4x$

$-3(bar(f(x)))= 4x-2$

$bar(f(x)) = (2-4x)/3$

Answer 2 · 2015-12-19T13:46:59

$f^-1(x)=-(4x-2)/3$

Rewrite as

$y=(2-3x)/4$

Flip the $x$ and $y$ and solve for $y$ .

$x=(2-3y)/4$

Multiply both sides by $4$ .

$4x=2-3y$

Subtract $2$ from both sides.

$4x-2=-3y$

Divide both sides by $-3y$ .

$-(4x-2)/3=y$

This can be rewritten in function notation, where $f^-1(x)$ represents an inverse function.

$f^-1(x)=-(4x-2)/3$

How do you find the inverse of f(x)=(2-3x)/4f(x)=(2-3x)/4?