Question

Which function has a restricted domain?

Answer 1

Hello!

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

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

A.  $f(x) = (3x)^{\frac{1}{5}} - 4$

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

B.  $k(x) = (-x + 3)^{\frac{1}{2}}$

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.