Question

question 24, 3.2.31 part 4 of 6 the graphs of two functions, f and g, are illustrated. use the graph to answer parts (a) through (f). (a) (f + g)(3)= 7 (simplify your answer.) (b) (f + g)(5)= 1 (simplify your answer.) (c) (f - g)(7)= 1 (simplify your answer.) (d) (g - f)(7)= (simplify your answer.)

Explanation:

Step1: Recall function - subtraction rule

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

Step2: Find $g(7)$ and $f(7)$ from the graph

From the graph, when $x = 7$, $g(7)=2$ and $f(7)=1$.

Step3: Calculate $(g - f)(7)$

Substitute $g(7)$ and $f(7)$ into the formula: $(g - f)(7)=g(7)-f(7)=2 - 1$.

Answer:

$1$