If f(x) is continuous in [-2,2]. wheref(x)= ll x+a, & x<0 , & 0 x<1, then -x, & x 1 .

If f(x) is continuous in [-2,2]. wheref(x)= ll x+a, & x<0 , & 0 x…

MCQ

If $f(x)$ is continuous in $[-2,2]$. where$f(x)=\left\{\begin{array}{ll}x+a, & x<0 \\x, & 0 \leq x<1, \text { then } \\b-x, & x \geq 1\end{array}\right.$

✓
a = 0, b = 2
B
a = 1, b = 2
C
a = 0, b = -2
D
a = -1, b = 2

✓

Answer

Correct option: A.

a = 0, b = 2

(A)
Since $f(x)$ is continuous in $[-2,2]$.
$\therefore $ it is continuous at $x=0$ and $x=1$.
$\therefore \lim _{x \rightarrow 0^{-}} f (x)=\lim _{x \rightarrow 0^{+}} f (x)$
$\Rightarrow \lim _{x \rightarrow 0^{-}}(x+a)=\lim _{x \rightarrow 0^{+}} x$
$\Rightarrow a=0$
Also, $\lim _{x \rightarrow 1^{-}} f (x)=\lim _{x \rightarrow 1^{+}} f (x)$
$\Rightarrow \lim _{x \rightarrow 1^{-}} x=\lim _{x \rightarrow 1^{+}}( b -x)$
$\Rightarrow l = b -1 \Rightarrow b=2$

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