Science:Math Exam Resources/Courses/MATH110/December 2013/Question 08/Statement

Let

$f(x)=\{\begin{array}{lr}{e}^{-x}& \text{if}x<t\\ 2(x+1)& \text{if}x\ge t\end{array}$

Explain why there exists a number $t$ such that $f$ is continuous.

(Hint: apply the Intermediate Value Theorem to the function $e^{-t}-2(t+1)$.)