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

2 Answers
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)

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