Question

Domain Find the domain of the function.

$k\left(x\right)=\frac{\sqrt{x+3}}{x-1}$

Short answer

The domain of the given function is $\left[-3,1\right)\cup \left(1,\infty \right)$.

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:

$k\left(x\right)=\frac{\sqrt{x+3}}{x-1}$

– Domain of the given function.

For$\sqrt{x+3}$ to be defined, we must have$x+3\ge 0$ that is $x\ge -3$.

In the given function$\frac{\sqrt{x+3}}{x-1}$ is undefined for $x-1=0$. It means $x\ne 1$.

The function is defined for all real values of x such that $-3\le x<1\text{\hspace{0.33em}or\hspace{0.33em}}1<x<\infty$.

Thus, the domain of the given function is $\left[-3,1\right)\cup \left(1,\infty \right)$.