Question
Find the relationship between $a$ and $b$ so that the function $f$ defined by$$f(x)=\left\{\begin{array}{ll}a x+1, & \text { if } x \leq 3 \\b x+3, & \text { if } x>3\end{array}\right.$$is continuous at $x=3$.
Step 1
This is given by $$\lim_{{x \to 3^-}} f(x) = \lim_{{x \to 3^-}} (ax+1) = a(3) + 1 = 3a + 1.$$ Show more…
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