Question

one table below shows some values of the domain and range for the function f(x)
the graph below shows y = g(x).
(a) evaluate
(i) f(2)
(ii) g(f(2))
(b) find f^{-1}(g(2))

Explanation:

Step1: Find $f(2)$ from table

From the table, when $x=2$, $f(2)=5$

Step2: Find $g(f(2))=g(5)$

From the graph, when $x=5$, $g(5)=3$

Step3: Find $g(2)$ from graph

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

Step4: Find $f^{-1}(4)$ (inverse function)

The inverse $f^{-1}(y)=x$ means find $x$ where $f(x)=4$. From the table, $f(3)=4$, so $f^{-1}(4)=3$

Answer:

(a) (i) $5$
(a) (ii) $3$
(b) $3$