Question

Find the domain of the real valued function: f(x) = log (x² - 4x + 3)

Answer 1

Answer:

$f(x)=log[{x}^2-4x+3]$

We know that logarithmic function is defined only for positive real numbers.

Hence f(x) is defined only when

${x}^2-4x+3$ is positive

That is, (x-1)(x-3) is positive

Thus, f(x) is defined for the values of x outside the interval (1,3)

Therefore, the domain of f(x) is R-(1, 3)

Answer 2

Answer:

Domain of f(x) : x > 1 or x < 3

it can be written as interval notation (-∞,1) ∪(3,∞)

Step-by-step explanation:

To find the domain of the real valued function: f(x) = log (x² - 4x + 3)

as we know that log function does not defined for negative values,so

x² - 4x + 3 > 0

x²-3x-x+3 > 0

x(x-3)-1(x-3) > 0

(x-3)(x-1) > 0

Domain of f(x) : x > 1 or x < 3

it can be written as interval notation (-∞,1) ∪(3,∞)