Solve y=f(x+c)

$$y = f ( x + c )$$

Solve for c

$$\left\{\begin{matrix}c=-x+\frac{y}{f}\text{, }&f\neq 0\\c\in \mathrm{R}\text{, }&y=0\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x+c.

$$y=fx+fc$$

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

$$fx+fc=y$$

Subtract fx from both sides.

$$fc=y-fx$$

Divide both sides by f.

$$\frac{fc}{f}=\frac{y-fx}{f}$$

Dividing by f undoes the multiplication by f.

$$c=\frac{y-fx}{f}$$

Divide y-xf by f.

$$c=-x+\frac{y}{f}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{y}{x+c}\text{, }&x\neq -c\\f\in \mathrm{R}\text{, }&y=0\text{ and }x=-c\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x+c.

$$y=fx+fc$$

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

$$fx+fc=y$$

Combine all terms containing f.

$$\left(x+c\right)f=y$$

Divide both sides by x+c.

$$\frac{\left(x+c\right)f}{x+c}=\frac{y}{x+c}$$

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

$$f=\frac{y}{x+c}$$