Question

Sketch the graph of the function $y=\frac{1}{2}{e}^{-x}-1$ and find domain of the function.

• A. Set of all naturals
• B. Set of all integers
• C. Set of all reals
• D. Set of all rationals

Answer 1

Answer: (C)

Set of all reals

The graph of the function $y=\frac{1}{2}{e}^{-x}-1$ is shown below.

Now we have to find the domain of $y=\frac{1}{2}{e}^{-x}-1$.

We know that, the domain is all the values that $x$ is allowed to take on.

So, here we have to find $e^{-x}$ is defined for what values of $x$.

We know that $e^{-x}$ is defined in $(-\infty ,\infty )$.

Therefore, the domain of $y=\frac{1}{2}{e}^{-x}-1$ is $(-\infty ,\infty )$ that is set of real numbers.