Q 3. - Precalculus Enhanced with Graphing Utilities

Question

What is the domain of $f\left(x\right)=\frac{x+5}{x^2+3x-18}$

Step-by-Step Solution

Answer

The domain of given function is $\mathrm{ℝ}-\left\{3,-6\right\}$

Step 1. Definition of domain

The domain of function is set of all possible values of $x$ that gives real values of $y$.

Step 2. Simplification

Given that $f\left(x\right)=\frac{x+5}{x^2+3x-18}$

$\Rightarrow f\left(x\right)=\frac{x+5}{\left(x-3\right)\left(x+6\right)}$

The vlue of $f\left(x\right)$ exist on all real numbers except $3$ and $-6$

So domain of given function is $\mathrm{ℝ}-\left\{3,-6\right\}$