Question

Consider continuous functions f and g. Then complete the statement.

(See attachment)

The x-intercept of the function f is (greater than, equal to, or less than) the x-intercept of function g.

(Multiple choice in the parentheses)

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Answer 1

Using the concept of x-intercept, it is found that the correct statement is:

• The x-intercept of the function f is greater than the x-intercept of function g.

What is the x-intercept of a function?

• The x-intercept of a function is the value of x when y = 0.

In this problem, in function f(x), when f(x) = 0, x = 3, hence the x-intercept is x = 3.

Function g(x) is defined by:

$g(x) = 2 + \sqrt[3]{3x + 1}$

Hence, the x-intercept of g(x) is found as follows:

$g(x) = 0$

$2 + \sqrt[3]{3x + 1} = 0$

$\sqrt[3]{3x + 1} = -2$

$(\sqrt[3]{3x + 1})^3 = (-2)^3$

$3x + 1 = -8$

$3x = -9$

$x = -\frac{9}{3}$

$x = -3$

The x-intercept of g(x) is -3, which is less than the x-intercept of function f(x), hence, the correct statement is:

• The x-intercept of the function f is greater than the x-intercept of function g.

To learn more about the concept of x-intercept, you can take a look at https://brainly.com/question/24737967