Let a function of domain equal to $\mathbb{R}$ be $f(x)=e^x-3$.
In which of the follows intervals, by the Bolzano theorem, we can say that $f(x)=-x-\frac{3}{2}$ have at least one solution?
$A) \left ]0,\frac{1}{5} \right[$
$B) \left ]\frac{1}{5},\frac{1}{4} \right[$
$C) \left ]\frac{1}{4},\frac{1}{3} \right[$
$D) \left ]\frac{1}{3},1 \right[$
At first I tried to solve $\space e^x-3=-x-\frac{3}{2}\space$ in order of $x$. I riched the equation $\space e^x+x=\frac{3}{2} \space$that I don't know how to solve, with the tools that I have learned.
I know that the$\space e^x-3=-x-\frac{3}{2}\space$ solution's is the intersept point beteewn the two functions. But I can't manage the solution using the Bolzano theorem principles.
Thanks for the help