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)(1)=1 (simplify your answer.) (b) (f + g)(3)= - 5 (simplify your answer.) (c) (f - g)(5)= (simplify your answer.)

the graphs of two functions, f and g, are illustrated. use the graph to answer parts (a) through (f). (a) (f + g)(1)=1 (simplify your answer.) (b) (f + g)(3)= - 5 (simplify your answer.) (c) (f - g)(5)= (simplify your answer.)

Answer

Explanation:

Step1: Recall function - operation formula

By the definition of function - subtraction, ((f - g)(x)=f(x)-g(x)). So, ((f - g)(5)=f(5)-g(5)).

Step2: Find (f(5)) from the graph

Looking at the graph of (y = f(x)), when (x = 5), the point on the graph of (f) is ((5,-2)), so (f(5)=-2).

Step3: Find (g(5)) from the graph

Looking at the graph of (y = g(x)), when (x = 5), the point on the graph of (g) is ((5,1)), so (g(5)=1).

Step4: Calculate ((f - g)(5))

Substitute (f(5)=-2) and (g(5)=1) into ((f - g)(5)=f(5)-g(5)), we get ((f - g)(5)=-2 - 1=-3).

Answer:

(-3)