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

Let

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

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

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