Question

Which description compares the domains of function A and Function B correctly?

Function A f(x) = log x
Function B
A - the domain of function A is the set of real numbers greater than or equal to 1
The domain of function B is the set of real numbers greater than 1
B- the domain of function A is the set of real numbers is greater than 0
The domain of the function B is the set of real numbers greater than or equal to 1
C- the domain of both functions is the set of real numbers
D- the domain of both functions is the set of real numbers greater than or equal to 1

Answer 1

Choice B is correct; the domain of function A is the set of real numbers greater than 0

The domain of the function B is the set of real numbers greater than or equal to 1

Explanation:

The domain of a function refers to the set of x-values for which the function is real and defined. The graph of function B reveals that the function is defined when x is equal 1 and beyond; that is its domain is the set of real numbers greater than or equal to 1.

On the other hand, the natural logarithm function is defined everywhere on the real line except when x =0; this will imply that its domain is the set of real numbers greater than 0 . In fact, the y-axis or the line x =0 is a vertical asymptote of the natural log function; meaning that its graph approaches this line indefinitely but neither touches nor crosses it.

Answer 2

You can use the definition of the domain of a function and the fact that the logarithm function only accepts positive quantity.

The description that compares the domain of function A and function B correctly is given by:

Option B- the domain of function A is the set of real numbers is greater than 0

The domain of the function B is the set of real numbers greater than or equal to 1

What is the domain of a function?

Domain of a function is a set which contains all the values for which the function is defined and outputs well defined value.

How to find the domain of given functions?

Taking the first function:

Function A: f(x) = log(x)

log never takes in non positive quantity. Thus we need to have x > 0

log is defined for all positive values of x.

Thus, the input can be any positive real number.

Or,

`Domain(log(x)) = \{x : x \in \mathbb R^+\} = \{x: x \in \mathbb R \: \& \: x > 0\}`

Taking the second function:

Function B: g(x) (plotted in given graph in question)

We can see that g(x) takes all values from x = 1 (it is between 0 and 2)

Assuming that the graph of g(x) keep being defined for rest of the values of x > 1, we get:

`Domain(g(x)) = \{x : x \in \mathbb R \: \& \: x \geq 1\}`

Thus, we have the correct description as:

Option B- the domain of function A is the set of real numbers is greater than 0

The domain of the function B is the set of real numbers greater than or equal to 1