Chapter 4: Q. 18 (page 225)

Find the domain of the rational function.
$Q (x) = \frac{- x (1 - x)}{3 x^{2} + 5 x - 2}$

Short Answer

Expert verified

The domain of the given function is

(- \infty, - 2) \cup (- 2, \frac{1}{3}) \cup (\frac{1}{3}, \infty)

Step by step solution

Step 1. Given information

The given function is $Q (x) = \frac{- x (1 - x)}{3 x^{2} + 5 x - 2}$

Step 2. Find the domain

For the domain, the denominator should not be equal to zero.

So,

$3 x^{2} + 5 x - 2 \neq 0 3 x^{2} + 6 x - x - 2 \neq 0 3 x (x + 2) - (x + 2) \neq 0 [t a k i n g o u t 3 x a n d - 1 a s c o m m o n] (3 x - 1) (x + 2) \neq 0 [t a k i n g o u t x + 2 a s c o m m o n] 3 x - 1 \neq 0 3 x \neq 1 x \neq \frac{1}{3} o r x + 2 \neq 0 x \neq - 2$

Thus, the domain of the given function is all real numbers except $- 2$ and $\frac{1}{3}$ .

Therefore, the domain is $(- \infty, - 2) \cup (- 2, \frac{1}{3}) \cup (\frac{1}{3}, \infty)$

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Find the domain of the rational function.
$Q (x) = \frac{- x (1 - x)}{3 x^{2} + 5 x - 2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the domain

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Find the domain of the rational function.
$Q (x) = \frac{- x (1 - x)}{3 x^{2} + 5 x - 2}$