Q. 7 - Precalculus Enhanced with Graphing Utilities

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 _________.

Step-by-Step Solution

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 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,

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