Function `f(x)={x-1, x<2 and 2x-3, xgeq2` is a continuous function

Options

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

Answer

C

Explanation

Since, it is a polynomial function, so it is continuous for every value of x except at x = 2
LHL `=underset(xto2^(-))limx-1=underset(hto0)lim2-h-1=1`
RHL `=underset(xto2^(+))lim2x-3`
`underset(hto0)lim2(2+h)-3=1`
and `" "f(2)=2(2)-3=1`
`:." "LHL=RHL =f(2)`
Hence, f(x) is continuous for all real values of x.