domain of f(x)=(1-e^{x^2})/(1-e^{1-x^2)}

⚠ f(x)=(1-e^{x^2})/(1-e^{1-x^2)} is read as f(x)=(1-e^(x^2))/(1-e^(1-x^2))

We save the definition:

f (x) = \frac{1 - e^{x^{2}}}{1 - e^{(1 - x^{2})}}

Let's find the domain of

\frac{1 - e^{x^{2}}}{1 - e^{(1 - x^{2})}}

For the expression

\frac{1 - e^{x^{2}}}{1 - e^{(1 - x^{2})}}

to be defined, we must have:

1 - e^{(1 - x^{2})} \neq 0

You can apply the ln function on both sides:

\ln (e^{(1 - x^{2})}) \neq \ln (1)

ℹ

\ln (e^{(1 - x^{2})})

1 - x^{2}

‖

\ln (1)

0

1 - x^{2} \neq 0

▶Domain of definition:

x \in ℝ \ {-1, 1}