state gov RPSC 2nd Grade Senior Teacher Mock Test Series 2025 Mathematics Limit and Continuity Continuity of a function
Let g(x) be a linear function and \(\rm f(x)=\left\{\begin{matrix}g(x)&, x\le 0\\\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}}&,x>0\end{matrix}\right.\) is continuous at x = 0 If f'(1) = f(-1), then the value of g(3) is
1
\(\rm \frac{1}{3}\log_e\left(\frac{4}{9e^{1/3}}\right)\)
2
\(\rm \frac{1}{3}\log_e\left(\frac{4}{9}\right)+1\)
3
\(\log_e\left(\frac{4}{9}\right)-1\)
4
\(\log_e\left(\frac{4}{9e^{1/3}}\right)\)
5
Question Not Attempted