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Find the relationship between 'a' and 'b' so that the function 'f' defined by $ f(x) = \left\{ \begin{array}{l l}ax+1, & \quad if { x \leq 3} \\ bx+3, & \quad if { x > 3} \end{array} \right. $ is continuous at x = 3.

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  • If $f$ is a real function on a subset of the real numbers and $c$ be a point in the domain of $f$, then $f$ is continuous at $c$ if $\lim\limits_{\large x\to c} f(x) = f(c)$.
Step 1:
At $x=3$
LHL=$\lim\limits_{\large x\to 3^-}(ax+1)$
RHL=$\lim\limits_{\large x\to 3^+}(bx+3)$
$f$ is continuous if LHL=RHL=f(3)
Step 2:
For any arbitrary value of $b$ we can find the value of $a$ corresponding the value of $b$.
answered Nov 12, 2013 by sreemathi.v

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