Chapter 4: Q. 17 (page 225)

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

Short Answer

Expert verified

The domain of the given function is $(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, 3) \cup (3, \infty)$

Step by step solution

Step 1. Given information

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

Step 2. Find the domain

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

So,

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

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

Therefore, the domain islocalid="1646075792279" $(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, 3) \cup (3, \infty)$

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

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. F(x)=3xx-12x2-5x-3

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Most popular questions from this chapter

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