Question

Which function has a restricted domain?

Answer 1

Hello!

`\large\boxed{\text{B. } k(x) = (-x + 3)^{(1)/(2) }}}`

We can look at each answer choice to verify whether it has a restricted domain or not:

A.
`f(x) = (3x)^{(1)/(5)} - 4`

This is a function similar to a cubic root function. Its domain is (-∞, ∞), so it has no restriction.

B.
`k(x) = (-x + 3)^{(1)/(2)}`

This is a square root function. This graph only consists of x-values in the interval (3, ∞) because you cannot take the square root of a negative number. This function has a restricted domain.

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

This is a cubic function, so it has an interval of (-∞, ∞)

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

This is a quadratic function, which has no domain restriction.

Therefore, the correct answer is B.