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Chapter 4: Q. 21 (page 225)

Find the domain of the rational function.
$H (x) = \frac{3 x^{2} + x}{x^{2} + 4}$

Short Answer

Expert verified

The domain of the function is all real numbers. i.e., $(- \infty, \infty)$

Step by step solution

01

Step 1. Given information

The given function is $H (x) = \frac{3 x^{2} + x}{x^{2} + 4}$

02

Step 2. Find the domain

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

so,

$x^{2} + 4 \neq 0 x^{2} \neq - 4$

There is no solution of this equation.

So, The domain of the function is all real numbers. i.e., $(- \infty, \infty)$

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Most popular questions from this chapter

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

$f (x) = 2 x^{5} - x^{4} - x^{2} + 1$

In Problems 57– 62, find the real zeros of f. If necessary, round to two decimal places.

$f (x) = x^{3} + 42.2 x^{2} - 664.8 x + 1490.4$

In Problems 57– 62, find the real zeros of f. If necessary, round to two decimal places.

$f (x) = x^{4} + 1.2 x^{3} - 7.46 x^{2} - 4.692 x + 15.2881$

Solve the given inequality algebraically.

$x^{3} > 1$

Find the domain of the rational function.

$G (x) = \frac{6}{(x + 3) (4 - x)}$

See all solutions

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