Solve f^-1(x)=x^5-6

$$f ^ { - 1 } ( x ) = x ^ { 5 } - 6$$

Solve for f

$$f=-\frac{x}{6-x^{5}}$$

$$x\neq 0\text{ and }x\neq \sqrt[5]{6}$$

Steps for Solving Linear Equation

Reorder the terms.

$$\frac{1}{f}x=x^{5}-6$$

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

$$1x=fx^{5}+f\left(-6\right)$$

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

$$fx^{5}+f\left(-6\right)=1x$$

Reorder the terms.

$$fx^{5}-6f=x$$

Combine all terms containing f.

$$\left(x^{5}-6\right)f=x$$

Divide both sides by x^{5}-6.

$$\frac{\left(x^{5}-6\right)f}{x^{5}-6}=\frac{x}{x^{5}-6}$$

Dividing by x^{5}-6 undoes the multiplication by x^{5}-6.

$$f=\frac{x}{x^{5}-6}$$

Variable f cannot be equal to 0.

$$f=\frac{x}{x^{5}-6}\text{, }f\neq 0$$