Chapter 4: Q. 6 (page 234)

$R (x) = \frac{x {(x - 2)}^{2}}{x - 2}$
Find the domain of $R$ .
Find the $x$ -intercepts of $R$ .

Short Answer

Expert verified

The domain of $R$ is, $\{x | x \neq 2\}$ .
The $x$ -intercepts of $R$ is $x = 0$ .

Step by step solution

Part a Step 1 Given equation is,

$R (x) = \frac{x {(x - 2)}^{2}}{x - 2}$

First find the zeros of the denominator.

$x - 2 = 0 x = 2$

The domain of $R$ is the set of all the real numbers except when $x = 2$ .

Part b Step 2 Substitute Rx=0 in the given equation.

$0 = \frac{x {(x - 2)}^{2}}{x - 2} x (x - 2) = 0 x = 2, 0$

As $2$ is not in the domain, the value of $x$ -intercept is $0$ .

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$R (x) = \frac{x {(x - 2)}^{2}}{x - 2}$
Find the domain of $R$ .
Find the $x$ -intercepts of $R$ .

Short Answer

Step by step solution

Part a Step 1 Given equation is,

Part b Step 2 Substitute Rx=0 in the given equation.

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Rx=xx-22x-2Find the domain of R.Find thex-intercepts ofR.

Short Answer

Step by step solution

Part a Step 1 Given equation is,

Part b Step 2 Substitute Rx=0 in the given equation.

One App. One Place for Learning.

Most popular questions from this chapter

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$R (x) = \frac{x {(x - 2)}^{2}}{x - 2}$
Find the domain of $R$ .
Find the $x$ -intercepts of $R$ .