How do you find the inverse of #y=(3x-7)/(x+9)#?

2 Answers
Manasvini Nittala
Apr 17, 2018

#f^-1(x)=(9x+7)/(3-x)#

Explanation:

let, #y=f(x)=(3x-7)/(x+9)# then we have
#x=f^-1(y)#
#rArry=(3x-7)/(x+9)rArry(x+9)=3x-7rArrxy+9y=3x-7#
#rArr9y+7=x(3-y)rArrx=(9y+7)/(3-y)#
since #x=f^-1(y)rArrf^-1(y)=(9y+7)/(3-y)rArrf^-1(x)=(9x+7)/(3-x)#

Elias
Apr 17, 2018

#f(x)^-1= (-9x-7)/(3+x)#

Explanation:

The inverse of a function switches the imput value and the output value. One easy way to solve inverse functions is by simply switching where the #x's and y's are #. So...
#f(x) = (3x-7)/(x+9) # turns into # x = (3y-7)/(y+9)#
Then from here on it is basic algebra.
# x = (3y-7)/(y+9)#
#x*(y+9) =( 3y-7)#
#xy+9x = 3y -7 #
#3y+xy = -9x-7#
#y(3+x)=-9x-7#
#f(x)^-1= (-9x-7)/(3+x)#

If you need any more of an explanation, I will add them in

Related questions
Impact of this question
1307 views around the world
You can reuse this answer
Creative Commons License