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Chapter 5: Q 3. (page 267)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Definition of domain

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

02

Step 2. Simplification

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

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

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

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

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Most popular questions from this chapter

Solve the equation $5^{x} = 5^{- 6}$

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