Solve f^-1(u)=1/u

$$f ^ { - 1 } ( u ) = \frac { 1 } { u }$$

Solve for f

$$f=u^{2}$$

$$u\neq 0$$

Solution Steps

Multiply both sides of the equation by u.

$$f^{-1}uu=1$$

Multiply u and u to get u^{2}.

$$f^{-1}u^{2}=1$$

Reorder the terms.

$$\frac{1}{f}u^{2}=1$$

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

$$1u^{2}=f$$

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

$$f=1u^{2}$$

Reorder the terms.

$$f=u^{2}$$

Variable f cannot be equal to 0.

$$f=u^{2}\text{, }f\neq 0$$

Solve for u (complex solution)

$$u=-\sqrt{f}$$

$$u=\sqrt{f}\text{, }f\neq 0$$

Solve for u

$$u=\sqrt{f}$$

$$u=-\sqrt{f}\text{, }f>0$$