If f(x) = l a x^2 - b, , ,when , , , , 0 x < 1 , , , , , , , , , … - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}a{x^2} - b,\,\,when\,\,{\rm{\,\, }}0 \le x < 1\\\,\,\,\,\,\,\,\,\,\,\,\,\,2,\;\,when\,\,{\rm{ }}x = 1\\\,\,\,\,\,x + 1,\,\,\,when\,{\rm{ \,\,1}} \,\, < x \le 2\end{array} \right.$ is continuous at $x = 1$, then the most suitable value of $a, b$ are

A
$a = 2,\;b = 0$
B
$a = 1,\;b = - 1$
C
$a = 4,\;b = 2$
✓
All the above

✓

Answer

Correct option: D.

All the above

d
(d) $\mathop {\lim }\limits_{x \to 1 - } f(x) = a - b,\,\,\mathop {\lim }\limits_{x \to 1 + } f(x) = 2\,\, \Rightarrow a - b = 2$

All the given sets of $a, b$ make $f(x)$ continuous at $x=1$.

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