Question

Find domain of the function
$f(x) = \frac{{x}^{2} + 3x + 5}{ {x}^{2} - 5x + 4}$


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Answer 1

Domain of f(x) is R-{1,4}

Answer 2

Answer:

x ≠ 4, x ≠ 1

Step-by-step explanation:

Method - 1:

Given: f(x) = (x² + 3x + 5)/(x² - 5x + 4)

For the domain, the denominator must be ≠ 0.

Since we cannot have a zero in the denominator, we will first find out which numbers make the denominator zero.

Set up the equation to solve for x:

⇒ x² - 5x + 4 = 0

⇒ x² - 4x - x + 4 = 0

⇒ x(x - 4) - (x - 4) = 0

⇒ (x - 1)(x - 4) = 0

⇒ x = 1, 4

Excluding these values from the domain, we get x ≠ 4, x≠ 1.

Domain : (-∞,1) ∪ (1,4) ∪ (4,∞), {x|x ≠ 1,4} for any integer n

Range: (-∞,∞), {y|y ∈ R}.

Hope it helps!