Let {\f}: {R} \rightarrow {R} and {\g}: {R} \rightarrow {R} be defined as f(x)={\\begin{array}{ccc}\log _e x & { & \\\\end{array} , x>0 ; e^{-x} ,{, } , x \leq 0}. and g(x)={\\begin{array}{ccc}x & { & \\\\end{array} , x \geq 0 ; e^x ,{, } , x< 0}. Then, gof : {R} \rightarrow {R} is : [1-Feb-2024 Shift 1]

Correct Answer is : neither one-one nor onto

JEE Main 1-Feb-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 11 of 90

Marks: +1, -0

Let f:R⟶R and g:R⟶R be defined as

f(x)={

logex	,‌	x>0
e−x	,‌	x≤0

.
and
g(x)={

x	,‌	x≥0
ex	,‌	x<0

.
Then, gof : R⟶R is :

[1-Feb-2024 Shift 1]

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f(x)	f(x)≥0
ef(x)	f(x)<0