How do you find the inverse of #f(x) =( -2x)/(-7-x)#?

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Answer 1 · 2015-10-23T04:31:37

#f^-1 (x)= (-7x)/(-2-x)#

First, change the term #f(x)# to #y#

Then, switch the x and y values. You should get
#x=(-2y)/(-7-y)#

Next solve for Y
-multiply x on the left side by #(-7-y)# to get rid of the denominator, you should get
#-7x-yx=-2y#

Lastly change the term #y# to #f^-1 (x)# [f inverse of x]
#f^-1 (x)= (-7x)/(-2-x)#