Solve f(x)^-1=x^3+1/2

$$f ( x ) ^ { - 1 } = \frac { x ^ { 3 } + 1 } { 2 }$$

Solve for f

$$f=\frac{x\left(x^{3}+1\right)}{2}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2fx^{-1}=x^{3}+1$$

Reorder the terms.

$$2\times \frac{1}{x}f=x^{3}+1$$

Multiply both sides of the equation by x.

$$2\times 1f=xx^{3}+x$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$2\times 1f=x^{4}+x$$

Multiply 2 and 1 to get 2.

$$2f=x^{4}+x$$

Divide both sides by 2.

$$\frac{2f}{2}=\frac{x^{4}+x}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$f=\frac{x^{4}+x}{2}$$