Find the inverse

Question

Find the inverse of f(x)= x-2/1+8x

Answer 1

Hi Pauline,

You want to swap x and y initially: x=(y-2)/(1+8y)

Now, solve for y. Notice that there are two of them, however. You want to multiply the denominator by x and set it equal to the numerator: x(1+8y)=y-2.

Distribute: x+8xy=y-2.

Subtract y from both sides and subtract x from both sides: 8xy-y=-x-2.

Now you can factor out a y so that it's singular in the equation: y(8x-1)=-x-2

Divide both sides by "8x-1": y^-1= (-x-2)/(8x-1) or y^-1=(x+2)/(1-8x).

The original function is one-to-one so you don't have to worry about domain restrictions.

I hope this helps!