the graphs of two functions, f and g, are illustrated. use the graph to answer parts (a) through (f). (a) (f…
the graphs of two functions, f and g, are illustrated. use the graph to answer parts (a) through (f). (a) (f + g)(4)= (simplify your answer.)
Answer
Explanation:
Step1: Recall function - sum formula
By the definition of the sum of two functions, $(f + g)(x)=f(x)+g(x)$. So, $(f + g)(4)=f(4)+g(4)$.
Step2: Find $f(4)$ from the graph
Looking at the graph of $y = f(x)$, when $x = 4$, the $y$-value of the function $f$ is $f(4)=4$.
Step3: Find $g(4)$ from the graph
Looking at the graph of $y = g(x)$, when $x = 4$, the $y$-value of the function $g$ is $g(4)= - 2$.
Step4: Calculate $(f + g)(4)$
Substitute $f(4)=4$ and $g(4)=-2$ into the formula $(f + g)(4)=f(4)+g(4)$. Then $(f + g)(4)=4+( - 2)=2$.
Answer:
2