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#