Question

If $f\left(x\right)=x+1$and $g\left(x\right)=x^3$, then____________ =$x^3-(x+1)$.

Short answer

If $f\left(x\right)=x+1$and $g\left(x\right)=x^3$, then $\mathbf{(}\mathit{g}\mathbf{-}\mathit{f}\mathbf{)}\mathbf{\left(}\mathit{x}\mathbf{\right)}$=$x^3-(x+1)$

Step-by-step solution

Step 1. Given information 

If $f\left(x\right)=x+1$and $g\left(x\right)=x^3$, then____________ =$x^3-(x+1)$

Step 2. DEFINITION

The difference $f-g$is the function defined by

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

Step 3. The value of f(x)=x+1 and g(x)=x3

$$\begin{gathered} (g-f)\left(x\right)=g\left(x\right)-f\left(x\right) \\ (g-f)\left(x\right)=x^3-(x+1) \end{gathered}$$