Solve f^-1(y)=3^y+1

$$f ^ { - 1 } ( y ) = 3 ^ { y } + 1$$

Solve for f

$$f=\frac{y}{3^{y}+1}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Reorder the terms.

$$\frac{1}{f}y=3^{y}+1$$

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by f.

$$1y=f\times 3^{y}+f$$

Swap sides so that all variable terms are on the left hand side.

$$f\times 3^{y}+f=1y$$

Reorder the terms.

$$f\times 3^{y}+f=y$$

Combine all terms containing f.

$$\left(3^{y}+1\right)f=y$$

Divide both sides by 3^{y}+1.

$$\frac{\left(3^{y}+1\right)f}{3^{y}+1}=\frac{y}{3^{y}+1}$$

Dividing by 3^{y}+1 undoes the multiplication by 3^{y}+1.

$$f=\frac{y}{3^{y}+1}$$

Variable f cannot be equal to 0.

$$f=\frac{y}{3^{y}+1}\text{, }f\neq 0$$