If the function $f:R ightarrow R$ given by $f(x) = \left\{ \begin{array}{r} x + a,\ if\ x \leq 1 \ 3 - x^{2},\ \ if\ x 1 \end{array} ight.\$ is continuous at $x = 1$, thyen $a$ is equal to

Question

If the function $f:R ightarrow R$ given by $f(x) = \left\{ \begin{array}{r} x + a,\ if\ x \leq 1 \ 3 - x^{2},\ \ if\ x > 1 \end{array} ight.\$ is continuous at $x = 1$, thyen $a$ is equal to

Dr. Abubacker · Accepted Answer

(d)
LHL$= \lim_{x \rightarrow 1^{-}}f(x) = \lim_{h \rightarrow 0}1 - h + a = 1 + a$
RHL$= \lim_{x \rightarrow 1^{+}}f(x) = \lim_{h \rightarrow 0}3 - (1 + h)^{2} = 2$
For $f(x)$ to be continuous, LHL=RHL
$\Rightarrow 1 + a = 2\ \ \ \  \Rightarrow \ \ \ a = 1$

Q. If the function $f:R \rightarrow R$ given by $f(x) = \left\{ \begin{array}{r} x + a,\ if\ x \leq 1 \\ 3 - x^{2},\ \ if\ x > 1 \end{array} \right.\$ is continuous at $x = 1$, thyen $a$ is equal to

Explanation

Reviewed by Dr. Abubacker

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