Number of solutions using graph

Question

We have to find the number of solutions of $e^((-x^(2))/2)$ + $-x^2 =0$

I tried it and got one solutions by drawing graph.

Is I have done correct ?

My try is on :

Answer 1

Short anwer to your question is: no

The long answer: your drawing of $e^{x^2/2}$ is incorrect. You have drawn a logarithmic function. What you need is a Gaussian curve. See: https://en.wikipedia.org/wiki/Gaussian_function

If you then draw $x^2$, you see that there are two points where the graphs coincide and this will give you your answer.

Answer 2

Since your drawing is of low quality, see the figures below.

Note that in the transformation to the log form, you forget a solution because it is not $\ln(x)$ but $\ln|x|$ (the absolute value of $x$). Do not forget the branch $\ln(-x)$ for the range $x<0$.