Calculus Examples

$f (x) = \frac{x - e^{2 x^{2}}}{e - x - e^{2 - x^{2}}}$

Step 1

Set the denominator in $\frac{x - e^{2 x^{2}}}{e - x - e^{2 - x^{2}}}$ equal to $0$ to find where the expression is undefined.

$e - x - e^{2 - x^{2}} = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 0.85273129, 1.27900791, 2.71359787$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, - 0.85273129) \cup (- 0.85273129, 1.27900791) \cup (1.27900791, 2.71359787) \cup (2.71359787, \infty)$

Set-Builder Notation:

${x | x \neq - 0.85273129, 1.27900791, 2.71359787}$

Step 4