Question

Find the domain of the function \(f\left( x \right) = \frac{{x + 1}}{{x^2 - 5x + 6}}\)
1. For all the real values except -1 and 2
2. For all the real values except 2 and 3
3. For all the real values except 3 and -1
4. For all the real values except -2 and -3

Answer 1

Correct Answer - Option 2 : For all the real values except 2 and 3

Concept:

Domain of \(\rm \frac {f(x)}{g(x)}\) is g(x) ≠ 0

Calculation:

If the denominator is not equal to zero, then only the function will be defined for the values.

For the function \(f\left( x \right) = \frac{{x + 1}}{{x^2 - 5x + 6}}\)

x² - 5x + 6 ≠ 0

⇒ x² - 3x - 2x + 6  ≠ 0

⇒ (x - 3)(x - 2) ≠ 0

⇒ x ≠ 2, 3

Therefore, the domain of the function is all real numbers except 2 and 3.