the graph below shows the functions f(x) and g(x). use the values in the graph to compute the following…
the graph below shows the functions f(x) and g(x). use the values in the graph to compute the following compositions. a) f(g(-1/2)) b) f(f(0))
Answer
Explanation:
Step1: Find $g(-\frac{1}{2})$ from the graph
From the graph, when $x =-\frac{1}{2}=-0.5$, $g(-0.5)= - 1.0$.
Step2: Find $f(g(-\frac{1}{2}))$
Since $g(-\frac{1}{2})=-1.0$, we find the value of $f(x)$ when $x = - 1.0$. From the graph of $f(x)$, when $x=-1.0$, $f(-1.0)\approx - 2.5$.
Step3: For $f(f(0))$, first find $f(0)$
From the graph of $f(x)$, when $x = 0$, $f(0)\approx1.5$.
Step4: Then find $f(f(0))$
Since $f(0)\approx1.5$, we find the value of $f(x)$ when $x = 1.5$. From the graph of $f(x)$, when $x = 1.5$, $f(1.5)\approx3.5$.
Answer:
a) $f(g(-\frac{1}{2}))\approx - 2.5$ b) $f(f(0))\approx3.5$