Here are the steps to find the inverse of an equation:
- Change g(x) to y
- Switch the positions of x and y
- Solve for y
- Change y to g^-1(x)
First, let's apply the first two steps:
[tex]g(x)=-4x+1\\y=-4x+1\\x=-4y+1[/tex]
Next, let's solve for y. Firstly, subtract 1 on both sides of the equation:
[tex]x-1=-4y[/tex]
Next, divide both sides by -4:
[tex]\frac{x-1}{-4}=y[/tex]
Now that we have solved for y, apply the last step and your answer will be [tex]g^{-1}(x)=\frac{x-1}{-4}[/tex]
