Question

Domain Find the domain of the function.

$h\left(x\right)={\left(x-3\right)}^{-\frac{1}{4}}$

Short answer

The domain of the given function is $\left(3,\infty \right)$.

Step-by-step solution

– Domain of a function.

Domain of a function is the set of all possible input values.

– Given information.

The given function is:

$h\left(x\right)={\left(x-3\right)}^{-\frac{1}{4}}$

– Domain of the given function.

The given function can be rewritten as;

$h\left(x\right)=\frac{1}{{\left(x-3\right)}^{\frac{1}{4}}}$

The value function is defined for all real values x such that

$\begin{array}{c}x-3>0\\ x>3\end{array}$

Thus, the domain of the given function is $\left(3,\infty \right)$.