Question

F ( g ( 0 ) ) = g ( f ( 2 ) ) = f ( f ( 5 ) ) = g ( g ( 1 ) ) =

Answer 1

Given: The graph of functions f(x) and g(x)

To Determine: The value of

`\begin{gathered} (a)\text{ }f(g(0)) \\ (b)g(f(2)) \\ (c)f(f(5)) \\ (d)g(g(1)) \end{gathered}`

Solution

(a)

`f(g(0))`

g(0) can be determined by checking g(x) function graph. the value of y when x = 0

`\begin{gathered} x=0,g(0)=2 \\ f(g(0))=f(2) \\ x=2,f(2)=5 \end{gathered}`

Therefore,

`f(g(0))=5`

(b)

`\begin{gathered} g(f(2))) \\ x=2,f(2)=5 \\ g(f(2))=g(5) \\ x=5,g(5)=4 \end{gathered}`

Therefore

`g(f(2))=4`

(c)

`\begin{gathered} f(f(5)) \\ x=5,f(5)=3 \\ f(f(5))=f(3) \\ x=3,f(3)=4 \end{gathered}`

Therefore

`f(f(5))=4`

(d)

`\begin{gathered} g(g(1)) \\ x=1,g(1)=1 \\ g(g(1))=g(1) \\ x=1,g(1)=1 \end{gathered}`

Therefore,

`g(g(1))=1`

Hence,