The graph of the function f(x)= 2x is shown. The inverse is also a function. If the domain of the inverse is the range values of the original function, identify the domain of the inverse of f(x).

A) {any real number}
B) {any real number > 0}
C) {any real number < 0}
D) {any real number ≥ 0}

option A is true.

Step-by-step explanation:

Given the function

As

The function has no undefined points nor domain constraints. Therefore, the domain is:

Therefore,

The range of polynomials with odd degree is all the real numbers.

Therefore,

as

Therefore,

Finding the domain of .

Again the function   has no undefined points nor domain constraints. Therefore, the domain is:

Therefore, the domain of the inverse of f(x) is:

Also the domain of the inverse is the range values of the original function.

Thus, the domain of the inverse of f(x) is the set of any real number, which can also be denoted as:  

Therefore, option A is true.

b

Step-by-step explanation:

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.