Question

2. A function g(x) is defined by the diagram shown below.

(a) What is the value of g(7)?

(b) What is the range of g(x)?

(c) Why would the inverse of g(x) not be a function? Explain.

Answer 1

Explanation:

diagram attached represents a function g(x).

Circle (1) (circle on the left) represents the set of domain (input values) and circle (2) represents the range (output values).

a). For input value x = 7, out put value of the function is y = 9.

Therefore, g(7) = 9 will be the answer.

b). Range of the function g(x) is the set of output values.

Range: {12, 9, 9, 17}

c). Inverse of the function g(x) will have,

Domain: {12, 9, 9, 17}

Range: {4, 7, 10, 15}

For input value of x = 9, there are two output values y = 7, 10.

Since, "a function can't have two output values for the same input value".

Therefore, inverse of the function g(x) will not represent a function.