Chapter 5: Q. 3 (page 256)

Find the domain of the function $f (x) = \frac{x^{2} - 1}{x^{2} - 25}$ .

Short Answer

Expert verified

The domain of the function is $(- \infty, 5) \cup (- 5, 5) \cup (5, \infty)$ .

Step by step solution

Step 1. Given Information.

The given function is $f (x) = \frac{x^{2} - 1}{x^{2} - 25}$ .

Step 2. Find the domain.

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.

Step 3. The domain expression.

The function $x^{2} - 25 = 0 \Rightarrow x = - 5, 5$ .

The expression is $(- \infty, 5) \cup (- 5, 5) \cup (5, \infty)$ .

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Find the domain of the function $f (x) = \frac{x^{2} - 1}{x^{2} - 25}$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the domain.

Step 3. The domain expression.

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Find the domain of the function $f (x) = \frac{x^{2} - 1}{x^{2} - 25}$ .