If `f(x)={(ax^2+b ,0lex<1),(4,x=1),(x+3,1ltxge2))` then the value of`(a ,b)` for which `f(x)` cannot be continuous at `x=1,` is (a)`(2,2)` (b) `(3,1)`(c)`(4,0)` (d)`(5,2)`

Explanation

To determine the values of \( (a, b) \) for which the function \( f(x) \) is not continuous at \( x = 1 \), we need to analyze the function defined as follows:

\[
f(x) =
\begin{cases}
ax^2 + b & \text{for } 0 \leq x < 1 \\
4 & \text{for } x = 1 \\
x + 3 & \text{for } 1 < x \leq 2
...