Solve f^-1(x)=x+1/4

$$f ^ { - 1 } ( x ) = \frac { x + 1 } { 4 }$$

Solve for f

$$f=\frac{4x}{x+1}$$

$$x\neq 0\text{ and }x\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$4f^{-1}x=x+1$$

Reorder the terms.

$$4\times \frac{1}{f}x=x+1$$

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

$$4\times 1x=fx+f$$

Multiply 4 and 1 to get 4.

$$4x=fx+f$$

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

$$fx+f=4x$$

Combine all terms containing f.

$$\left(x+1\right)f=4x$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)f}{x+1}=\frac{4x}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$f=\frac{4x}{x+1}$$

Variable f cannot be equal to 0.

$$f=\frac{4x}{x+1}\text{, }f\neq 0$$

Solve for x

$$x=\frac{f}{4-f}$$

$$f\neq 4\text{ and }f\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$4f^{-1}x=x+1$$

Subtract x from both sides.

$$4f^{-1}x-x=1$$

Reorder the terms.

$$-x+4\times \frac{1}{f}x=1$$

Multiply both sides of the equation by f.

$$-xf+4\times 1x=f$$

Multiply 4 and 1 to get 4.

$$-xf+4x=f$$

Combine all terms containing x.

$$\left(-f+4\right)x=f$$

The equation is in standard form.

$$\left(4-f\right)x=f$$

Divide both sides by 4-f.

$$\frac{\left(4-f\right)x}{4-f}=\frac{f}{4-f}$$

Dividing by 4-f undoes the multiplication by 4-f.

$$x=\frac{f}{4-f}$$