Question

Select the correct answer.

Which function has a restricted domain?
O A. k(x) = (-x + 3)
OB.
j(z) = (3x) * - 4
O c.
h(x) = (4x)² - 5
h(r)
OD.
g(x) = -(x + 8)³

Answer 1

None of the given functions (A, B, C, D) has a restricted domain based on the information provided.

To identify the function with a restricted domain, we need to look for any restrictions on the values that the variable (in this case, x ) can take. The function with a restricted domain typically has some limitations on the possible input values.

Let's examine each function:

A.
`\( k(x) = (-x + 3) \)`

No restrictions mentioned or implied in the expression. The domain is not restricted.

B.
`\( j(z) = (3z) * -4 \)`

No restrictions mentioned or implied. The domain is not restricted.

C.
`\( h(x) = (4x)^2 - 5 \)`

The expression involves squaring
`\( 4x \)`, and squaring any real number always results in a non-negative value. Therefore, there are no restrictions on the domain.

D.
`\( g(x) = -(x + 8)^3 \)`

The expression involves cubing
`\( x + 8 \)`, and cubing any real number covers the entire real number line. Therefore, there are no restrictions on the domain.

In summary, none of the given functions (A, B, C, D) has a restricted domain based on the information provided.