Question

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

Function g is the sum of 2 and the cube root of the sum of three times x and 1.

Select the correct answer from each drop-down.

The x-intercept of function f is
the x-intercept of function g.

Answer 1

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

First, we need to write the statement Function g is the sum of 2 and the cube root of the sum of three times x and 1 as a function. This is expressed as:

• g(x) = $\sqrt[3]{3x+1} + 2$

• The x-intercept is the point where g(x)  = 0

Substituting this g(x) = 0 into the function will give:

$\sqrt[3]{3x+1} + 2 = 0\\\sqrt[3]{3x+1} = -2\\3x + 1 = -8\\3x = -9\\x = -3$

For the function f(x), the x-intercept is 3 from the given table.

Therefore, the x-intercept of function f is lower than the x-intercept of function g.

Learn more on intercept here: https://brainly.com/question/12271239

Answer 2

Answer:

the y-intercept of function f is less than the x-intercept of function g.

Step-by-step explanation: see attached