Question

If the domain of $f$is all real numbers in the interval $[0,7]$and the domain of g is all real numbers in the interval $[-2,5]$, the domain of $f+g$is all real numbers in the interval _________.

Short answer

If the domain of $f$is all real numbers in the interval$[0,7]$and the domain of g is all real numbers in the interval$[-2,5]$, the domain of$f+g$is all real numbers in the interval $\mathbf{[}\mathbf{0}\mathbf{,}\mathbf{5}\mathbf{]}$

Step-by-step solution

Step 1. Given information 

If the domain of $f$is all real numbers in the interval $[0,7]$and the domain of g is all real numbers in the interval $[-2,5]$, the domain of$f+g$ is all real numbers in the interval _________.

Step 2. Main Idea:

$\mathbf{Domain}\mathbf{}\mathbf{of}f+g=\mathbf{Domain}\mathbf{}\mathbf{of}f\cap \mathbf{Domain}\mathbf{}\mathbf{of}g$

Step 3. It is given that:

Domain of $f=[0,7]$

Domain of $g=[-1,5]$

Therefore,

$$\begin{gathered} f+g=[0,7]\cap [-1,5] \\ f+g=[0,5] \end{gathered}$$