Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 15, 2024

Find the other factor in the denominator when $x = -3$ is a restricted value for $f(x) = \frac{\text{anything}}{\text{not zero}}$ .

STEP 1

Assumptions
1. The function $f(x)$ has a domain restriction where $x \neq 5$ and $x \neq -3$ .
2. The denominator of $f(x)$ must not be zero.
3. The numerator of $f(x)$ can be any expression, as it is not restricted.

STEP 2

Since $x$ cannot be 5, we must ensure that the denominator of $f(x)$ becomes zero when $x = 5$ . To achieve this, we include a factor of $(x - 5)$ in the denominator.

STEP 3

Similarly, since $x$ cannot be -3, we must ensure that the denominator of $f(x)$ becomes zero when $x = -3$ . To achieve this, we include a factor of $(x - (-3))$ or $(x + 3)$ in the denominator.

STEP 4

Combining the factors from STEP_2 and STEP_3, we obtain the complete denominator of $f(x)$ that respects the domain restrictions.
$Denominator = (x - 5)(x + 3)$

STEP 5

The other factor in the denominator, corresponding to the restricted value of $x = -3$ , is therefore $(x + 3)$ .
i. The other factor here is: $x + 3$ .

Was this helpful?

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Contact Influencer program Policy Terms