state the domain of the following function in interval notation
f(x)=x^2-4x+3
explain how this is the answer
give step by step
The domain of a function is the set of all possible input values (x-values) that the function can take.
To determine the domain of the function f(x) = x^2 - 4x + 3, we need to consider what values of x will not cause any undefined operations in the function.
Step by step:
1. Consider any restrictions on the domain:
- Since there are no square roots or division by zero operations in the function, there are no restrictions on the domain.
2. Write the domain using interval notation:
- Since the function is a polynomial, it is defined for all real numbers. Therefore, the domain is all real numbers, which can be written in interval notation as (-∞, ∞).
Therefore, the domain of the function f(x) = x^2 - 4x + 3 is (-∞, ∞).