Question

the graphs of two functions, f and g, are illustrated. use the graph to answer parts (a) through (f). (a) (f + g)(3)= (simplify your answer.)

Explanation:

Step1: Recall function - sum property

By the definition of the sum of two functions, \((f + g)(x)=f(x)+g(x)\). So, \((f + g)(3)=f(3)+g(3)\).

Step2: Find \(f(3)\) from the graph

Looking at the graph of \(y = f(x)\), when \(x = 3\), the \(y\) - value of the point on the graph of \(f(x)\) is \(y=f(3)=6\).

Step3: Find \(g(3)\) from the graph

Looking at the graph of \(y = g(x)\), when \(x = 3\), the \(y\) - value of the point on the graph of \(g(x)\) is \(y = g(3)=1\).

Step4: Calculate \((f + g)(3)\)

Substitute \(f(3)=6\) and \(g(3)=1\) into \((f + g)(3)=f(3)+g(3)\). We get \((f + g)(3)=6 + 1=7\).

Answer:

7