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Function f(x)={(x-1",",x lt 2),(2x-3",",...

Function `f(x)={(x-1",",x lt 2),(2x-3",", x ge 2):}` is a continuous function

A

for x = 2 only

B

for all real values of x such that `x ne 2`

C

for all real values of x

D

for all integral values of x only

Text Solution

Verified by Experts

The correct Answer is:
C
Given function is `f(x)={(x-1",",x lt 2),(2x-3",",x ge 2):}`
Since, it is a polynomial function, so it is continuous for every value of x except possibly at x =2.
At x = 2, `LHL=lim_(x to 2^(-)) x-1=lim_(h to 0)2-h=1`
`RHL=lim_(x to 2^(+)) 2x-3`
`=lim_(h to 0)2(2+h)-3=1`
` and f(2)=2(2)-3=1`
`therefore LHL=RHL=f(2)`
Thus, f(x) is continuous for all real values of x.
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