Which of the following functions cannot receive a negative value of x when we are dealing exclusively with real numbers?

1. log(x)
2. exp(x)
3. sqrt(x)
4. 1/x

A.:

Just log(x) and sqrt(x).

Which of the following functions cannot receive a zero value of x when we are dealing exclusively with real numbers?

1. log(x)
2. exp(x)
3. sqrt(x)
4. 1/x

A.:

Just log(x) and 1/x.

How would you simplify the following expressions to reduce the chance of overflow, underflow, or just to be more efficient?

1. log(sqrt(x))
2. sqrt(exp(x))
3. 1/exp(x)

A.:

1. log(sqrt(x)) = log(x)/2
2. sqrt(exp(x)) = exp(x/2)
3. 1/exp(x) = exp(-x)