Question

the piecewise - linear function, f, defined on (0leq xleq8) is shown in the graph above. the function g is given by (g(x)=2x + 1). which of the following is approximately 3?
(\bigcirc f(f(4)))
(\bigcirc f(f(5)))
(\bigcirc f(g(4)))
(\bigcirc f(g(5)))

Explanation:

Step1: Find f(4) from the graph

From the graph, when $x=4$, $f(4)=3$.

Step2: Calculate f(f(4))

Substitute $f(4)=3$ into $f$: $f(f(4))=f(3)$. From the graph, $f(3)=2$.

Step3: Find f(5) from the graph

From the graph, when $x=5$, $f(5)=4$.

Step4: Calculate f(f(5))

Substitute $f(5)=4$ into $f$: $f(f(5))=f(4)=3$.

Step5: Calculate g(4)

Use $g(x)=2x+1$: $g(4)=2(4)+1=9$. Since $f(x)$ is only defined for $0\leq x\leq8$, $f(g(4))$ is undefined.

Step6: Calculate g(5)

Use $g(x)=2x+1$: $g(5)=2(5)+1=11$. Since $f(x)$ is only defined for $0\leq x\leq8$, $f(g(5))$ is undefined.

Answer:

$\boldsymbol{f(f(5))}$