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Let $f: R \rightarrow R$ be a function defined as
$f(x)=\left\{\begin{array}{ccc}
5 & , & \text { if } x \leq 1 \\
a+b x & , & \text { if } 1 < x < 3 \\
b+5 x & , & \text { if } 3 \leq x < 5 \\
30 & , & \text { if } x \geq 5
\end{array} \mid \text { then } f\right. \text { is }$
Options:
$f(x)=\left\{\begin{array}{ccc}
5 & , & \text { if } x \leq 1 \\
a+b x & , & \text { if } 1 < x < 3 \\
b+5 x & , & \text { if } 3 \leq x < 5 \\
30 & , & \text { if } x \geq 5
\end{array} \mid \text { then } f\right. \text { is }$
Solution:
1290 Upvotes
Verified Answer
The correct answer is:
not continuous for any values of $a$ and $b$.
for continuity at $x=1, a+b=5$
for continuity at $x=3, a+3 b=b+15$
$\Rightarrow a+2 b=15$
$\because$ system of equation (i), (ii) and (iii) is inconsistent Hence, $f(x)$ is not continuous for any values of $a$ and $b$ on $R$
for continuity at $x=3, a+3 b=b+15$
$\Rightarrow a+2 b=15$
$\because$ system of equation (i), (ii) and (iii) is inconsistent Hence, $f(x)$ is not continuous for any values of $a$ and $b$ on $R$
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