# For what value of the constants A and B is the function (ax+3) continuous for all X if x > 5?

Sep 8, 2016

$f \left(x\right) = a x + b$ is continuous for all Real (in fact all Complex) constant values of $a$ and $b$

#### Explanation:

The question is not clear but I have assumed:

$\textcolor{w h i t e}{\text{XXX}} \left(a x + 3\right)$ was meant to be $\left(a x + b\right)$

$\textcolor{w h i t e}{\text{XXX}}$capitalization of $A , B , \mathmr{and} X$ is irrelevant.
$\textcolor{w h i t e}{\text{XXX}} \left(A \equiv a\right) , \left(B \equiv b\right) , \mathmr{and} \left(X \equiv x\right)$

Any function of the form $f \left(x\right) = a x + b$ with constant values $a$ and $b$ is a linear function which is continuous for all values of $x$.
(The limitation $x > 5$ does not seem to be relevant).