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

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

Solve for f

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

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

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.

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

Multiply 4 and 1 to get 4.

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

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

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

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.

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