Chapter 2: Q. 4 (page 126)

Find the domain of each function and evaluate each function at $x = - 1$ .
role="math" localid="1645961084507" $h (x) = \frac{x - 4}{x^{2} + 5 x - 36}$

Short Answer

Expert verified

The domain of the function is $\{x | x \neq - 9, x \neq 4\}$

The value at $x = - 1$ is $\frac{1}{8}$

Step by step solution

Step 1. Find the domain of the function.

$h (x) = \frac{x - 4}{x^{2} + 5 x - 36}$

For domain, denominator cannot be zero.

So,

$x^{2} + 5 x - 36 \neq 0 x^{2} + 9 x - 4 x - 36 \neq 0 x (x + 9) - 4 (x + 9) \neq 0 (x + 9) (x - 4) \neq 0 x \neq - 9, 4$

Therefore, the domain of the function is $x$ belongs to all real numbers except $- 9, 4$ .

Step 2. Find value of h(x) at x=-1

$h (x) = \frac{x - 4}{x^{2} + 5 x - 36} h (- 1) = \frac{- 1 - 4}{{(- 1)}^{2} + 5 (- 1) - 36} h (- 1) = \frac{- 5}{- 40} h (- 1) = \frac{1}{8}$

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Find the domain of each function and evaluate each function at $x = - 1$ .
role="math" localid="1645961084507" $h (x) = \frac{x - 4}{x^{2} + 5 x - 36}$

Short Answer

Step by step solution

Step 1. Find the domain of the function.

Step 2. Find value of h(x) at x=-1

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Find the domain of each function and evaluate each function at x=-1.role="math" localid="1645961084507" h(x)=x-4x2+5x-36

Short Answer

Step by step solution

Step 1. Find the domain of the function.

Step 2. Find value of h(x) at x=-1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Probability and Statistics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the domain of each function and evaluate each function at $x = - 1$ .
role="math" localid="1645961084507" $h (x) = \frac{x - 4}{x^{2} + 5 x - 36}$