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Chapter 4: Q. 23 (page 225)

In Problems 13鈥�24, find the domain of each rational function.

R(x)=3(x2-x-6)4(x2-9)

Short Answer

Expert verified

The domain of the rational function R(x)=3(x2-x-6)4(x2-9) is {xx鈮�-3,x鈮�3}

Step by step solution

01

Step 1. Given

The rational function R(x)=3(x2-x-6)4(x2-9)

To find the domain of the given rational function.

02

Step 2. Factor the denominator.

Factorize the denominator.

4(x2-9)=4(x2-32)=4(x+3)(x-3)

03

Step 3. Use the zero-Product property

By using Zero-Product property,

(x+3)(x-3)=0

Either x+3=0or

x-3=0

04

Step 4. Solve the equation

Solve the equations

x+3=0x=-3

And x-3=0x=3

The domain of the function is {xx鈮�-3,x鈮�3}

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Most popular questions from this chapter

Graph each rational function using transformations.

R(x)=x-4x

Find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f.

f(x)=2x3-x2-11x-6

True or False : The graph off(x)=xx-3 is above the x-axis for x<0or x>3, so the solution set of the inequality xx-3鈮�0is {x:x鈮�0orx鈮�3}..

Find the real zeros of f. Use the real zeros to factor f.

f(x)=x3-8x2+17x-6

Find the real zeros of f. Use the real zeros to factor f.

f(x)=2x3-13x2+24x-9
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