Find the domain of the given function f. (Enter your answer using interval notation.)
f(x) = 1/(x2 − 8x + 16)
well, x cannot be 4 or the denominator will be zero, which is not allowed.
To find the domain of the function f(x) = 1/(x^2 - 8x + 16), we need to determine the values of x that make the denominator non-zero.
The denominator, x^2 - 8x + 16, can be factored as (x - 4)(x - 4) or (x - 4)^2.
For the denominator to be non-zero, (x - 4) should not equal to zero. This means x should not equal to 4.
Therefore, the domain of the function is all real numbers except x = 4.
In interval notation, the domain would be (-∞, 4) U (4, ∞).
To find the domain of the given function f(x) = 1/(x^2 − 8x + 16), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.
In this case, the denominator is a quadratic expression x^2 − 8x + 16. To determine if it can be equal to zero, we can find the roots of the quadratic equation.
The quadratic equation can be factored as (x - 4)(x - 4) = 0, which means that the function is equal to zero when x = 4.
Therefore, the only x-value that would result in division by zero is x = 4. Hence, the domain of the function f(x) is all real numbers except x = 4.
In interval notation, we can write the domain as (-∞, 4) U (4, ∞). This means that x can be any real number except 4.