Question

The function $‘f’$ is defined by $f(x)=2x-1$, if $x>2,f(x)=k$ if $x=2$ and $x^2-1$, if $x<2$ is continuous, then the value of k is equal to :

• A. 2
• B. 3
• C. 4
• D. -3

Answer 1

Answer: (B)

Let f is defined as $f(x)=2x-1$ if $x>2$
$=k$ if $x=2$
$=x^2-1$ if $x<2$
Since, f (x) is continuous.
$\therefore$ Limit of f (x) at x = 2 = value of f (x) at 2.
i.e., $\underset{x\to 2}{\lim }f(x)=f(2)$
Now, $\underset{x\to 2}{\lim }f(x)=\underset{x\to 2}{\lim }(2x-1)=3=f(2)$
But given $f(x)=k$ at $x=2$
$\therefore k=3$