Final answer:
The domain of the given function is all real numbers except for x = 1 and x = 4.
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, we are given a rational function, which means we need to find the x-values for which the denominator is not equal to 0. The denominator of the given function is x^2 - 5x + 4, so we need to find the x-values that make this expression not equal to 0.
To find these values, we can set the denominator equal to 0 and solve for x:
x^2 - 5x + 4 = 0
Factoring this quadratic equation, we get:
(x - 1)(x - 4) = 0
Setting each factor equal to 0, we find that x = 1 and x = 4 are the values that make the denominator equal to 0. Therefore, the domain of the function is all real numbers except for x = 1 and x = 4.
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