Chapter 7: Q. 371 (page 732)

Solve each rational function inequality and write the solution in interval notation.
Given the function $R (x) = \frac{(x - 5)}{(x - 2)}$ find the values of x that make the function less than or equal to 0.

Short Answer

Expert verified

Solution for inequality is $x \in (2, 5] .$

Step by step solution

Step 1. Given Information

The given rational function is denoted as $R (x) = \frac{(x - 5)}{(x - 2)} .$

Step 2. Critical point

To find the critical points,

$(x - 5) = 0 x = 5 (x - 2) = 0 x = 2$

To check the values,

$At x = 5, R (x) = \frac{0}{3}, R (x) = 0 At x = 2, R (x) = \frac{2 - 5}{0}, R (x) = \infty$

When the polynomial function is undefined, the critical point will not add in interval notation.

Step 3. Number line

On dividing the number line using critical point,

Step 4. Testing of polynomial expression

On testing the sign of polynomial expression and number line sign of factors.

Thus, $\frac{(x - 5)}{(x - 2)} \leq 0 is true for x \in (2, 5] .$

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Solve each rational function inequality and write the solution in interval notation.
Given the function $R (x) = \frac{(x - 5)}{(x - 2)}$ find the values of x that make the function less than or equal to 0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Critical point

Step 3. Number line

Step 4. Testing of polynomial expression

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Solve each rational function inequality and write the solution in interval notation.Given the functionR(x)=(x-5)(x-2)find the values of x that make the function less than or equal to 0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Critical point

Step 3. Number line

Step 4. Testing of polynomial expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Mechanics Maths

Applied Mathematics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each rational function inequality and write the solution in interval notation.
Given the function $R (x) = \frac{(x - 5)}{(x - 2)}$ find the values of x that make the function less than or equal to 0.