Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (a)/Solution 1

We first simplify using the exponential rules to get $f(x)=e^{x^3+2x^2+x-3}.$ Then we can solve for $f(x)=0$.

$\begin{array}{rl}{e}^{x^3+2x^2+x-3}& =0\\ x^3+2x^2+x-3& =\ln (0).\end{array}$

By taking the natural logarithm of both sides, we get a $\ln (0)$ on the right hand side which is bad since $0$ is not in the domain of the natural logarithm. So we conclude that there cannot be a solution to the equation $f(x)=0$. Hence, we have $0$ solutions.