Question

x | f(x)
-1 | \\(\frac{1}{2}\\)
0 | 1
1 | 2
2 | 4
the value of \\((f \circ g)(4)\\) is 2 ×.
when \\((g \circ f)(x) = 1\\), the value of x is 1 ×.

Explanation:

Step1: Find $g(4)$ from graph

From the graph of $g(x)$, when $x=4$, $g(4)=2$.

Step2: Compute $(f\circ g)(4)=f(g(4))$

Substitute $g(4)=2$ into $f(x)$: $f(2)=4$.

Step3: Solve $(g\circ f)(x)=1$, find $f(x)$ first

From the graph of $g(x)$, $g(y)=1$ when $y=0$, so $f(x)=0$.

Step4: Find $x$ where $f(x)=0$

Check the table for $f(x)$: no direct $f(x)=0$, but $g(f(x))=1$ means $f(x)$ is the input to $g$ that gives 1. Since $g(0)=1$, we need $f(x)=0$. Wait, correct: $g(z)=1$ when $z=0$, so $f(x)=0$. Looking at $f(x)$ values, the function is exponential: $f(x)=2^x$. Set $2^x=0$ no, wait: from graph, $g(0)=1$, so $f(x)=0$? No, wait, $g(1)=1$? No, graph: when $x=0$, $g(0)=0$; $x=1$, $g(1)=1$. Oh right! $g(1)=1$, so $f(x)=1$. From table, $f(0)=1$. So $x=0$.

Answer:

The value of $(f\circ g)(4)$ is $\boldsymbol{4}$.
When $(g\circ f)(x)=1$, the value of $x$ is $\boldsymbol{0}$.