JEE MAIN - Mathematics (2024 - 29th January Morning Shift - No. 10)
If $$f(x)=\left\{\begin{array}{cc}2+2 x, & -1 \leq x < 0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3\end{array} ; g(x)=\left\{\begin{array}{cc}-x, & -3 \leq x \leq 0 \\ x, & 0 < x \leq 1\end{array}\right.\right.$$, then range of $$(f o g)(x)$$ is
$$[0,1)$$
$$[0,3)$$
$$(0,1]$$
$$[0,1]$$
Explanation
$$f(g(x)) = \left\{ {\matrix{ {2 + 2g(x),} & { - 1 \le g(x) < 0} & {.....(1)} \cr {1 - {{g(x)} \over 3},} & {0 \le g(x) \le 3} & {.....(2)} \cr } } \right.$$
$$\text { By (1) } x \in \phi$$
And by (2) $$x \in[-3,0]$$ and $$x \in[0,1]$$
_29th_January_Morning_Shift_en_10_1.png)
Range of $$\mathrm{f(g(x))}$$ is $$[0,1]$$
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