Question

Are the functions $f\left(x\right)=x-1$and$g\left(x\right)=\frac{x^2-1}{x+1}$ the same? Explain.

Short answer

The both functions are same.

Step-by-step solution

Step 1. Given Information 

Are the functions $f\left(x\right)=x-1$ and$g\left(x\right)=\frac{x^2-1}{x+1}$ the same? Explain.

Step 2. The given functions are f(x)=x-1 and g(x)=x2-1x+1.

Firstly solving the function $g\left(x\right)$.

Using the formula $(a^2-b^2)=(a-b)(a+b)$

$$\begin{gathered} g\left(x\right)=\frac{(x-1)(x+1)}{x+1} \\ g\left(x\right)=x-1 \end{gathered}$$

Step 3. The both functions are same.

Both functions are same because when we solve the function$g\left(x\right)$, then$f\left(x\right)=g\left(x\right)$