Let {\g}( {\x}) be a linear function and f(x)={\\begin{array}{ccc}g(x) & { & \\\\end{array} x \leq 0 ; (\frac{1+x}{2+x}) ^{\frac{1}{x}} ,{, } x > 0}., is continuous at x=0. If f^{'}( 1)=f(-1), then the value of g( 3) is [31-Jan-2024 Shift 1]

Correct Answer is : loge(49e1∕3)

\frac{1}{3} \log _{ {\e}} ( {4}/{9 {\e}^{1 \/ 3}})

\frac{1}{3} \log _{ {\e}} (\frac{4}{9}) +1

\log _e (\frac{4}{9 e^{1 \/ 3}})

JEE Main 31-Jan-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 17 of 90

Marks: +1, -0

Let g(x) be a linear function and f(x)={

g(x)

,‌x≤0

(‌

1+x

2+x

)‌

,‌x>0

., is continuous at x=0. If f′(1)=f(−1), then the value of g(3) is

[31-Jan-2024 Shift 1]

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