Functions Question 5
Question 5 - 2024 (29 Jan Shift 1)
If $f(x)=\begin{array}{l}2+2 x,-1 \leq x<0 \\ 1-\frac{x}{3}, 0 \leq x \leq 3\end{array} ; g(x)=\begin{array}{l}-x,-3 \leq x \leq 0 \\ x, 0<x \leq 1\end{array}$,
then range of $(\operatorname{fog}(x))$ is
(1) $(0,1]$
(2) $[0,3)$
(3) $[0,1]$
(4) $[0,1)$
Show Answer
Answer (3)
Solution
By (1) $x \in \phi$
And by (2) $x \in[-3,0]$ and $x \in[0,1]$
Range of $f(g(x))$ is $[0,1]$
