Question

Given below are two statements
Statement-I : $f(x)=\begin{cases} \frac{3x-2}x \quad &\text{for 0≤x≤1}\\\ \frac{sin(x-1)}{x-1} \quad &\text{for} \,\, x>1 \\\ \end{cases}$
Function is continuous at x=1
Statement-II: $f(x)=\begin{cases} \frac{xe^\frac{1}x}{1+e^{\frac1{x}}} \quad &\ ; x\neq 0\\\ 0\quad &\text{; } \,\, x=0 \\\ \end{cases}$
Function is continuous at origin.
In the light of the above statements, choose the correct answer from the options given below.

• A. Both Statement-I and Statement-ll are true
• B. Both Statement-I and Statement-ll are false
• C. Statement-I is true but Statement-II is false
• D. Statement-I is false but Statement-II is true

Answer 1

Answer: (A)

Both Statement-I and Statement-ll are true

Answer 2

The Correct answer is option (A) : Both Statement-I and Statement-ll are true