How do you find the inverse of $f(x)=(x-4)/(33-x)$ ?

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Answer 1 · 2016-12-31T08:34:56

The inverse is $=(33x+4)/(1+x)$

Let $y=f(x)=(x-4)/(33-x)$

Then,

$y(33-x)=x-4$

$33y-xy=x-4$

$33y+4=x+xy$

$x(1+y)=33y+4$

$x=(33y+4)/(1+y)$

Therefore,

$f^(-1)(x)=(33x+4)/(1+x)$

Verification,

$f(f^(-1)(x))=f((33x+4)/(1+x))=((33x+4)/(1+x)-4)/(33-(33x+4)/(1+x))$

$=(33x+4-4-4x)/(33+33x-33x-4)$

$=(29x)/(29)$

$=x$

How do you find the inverse of f(x)=(x-4)/(33-x)f(x)=(x-4)/(33-x)?