contestada

Given no other restrictions, what are the domain and range of the following function?
f(x)=x^2-2x+3

Respuesta :

Using function concepts, it is found that:

  • The domain is all real values.
  • The range is: [tex](2, \infty)[/tex].

What are the domain and range of a function?

  • The domain of a function is the set that contains all possible input values.
  • The range of a function is the set that contains all possible output values.

For a quadratic function in the following format:

[tex]f(x) = ax^2 + bx + c[/tex]

  • The domain is all real values.
  • If a > 0, the range is [tex]\left(-\frac{b^2 - 4ac}{4a}, \infty\right)[/tex].

In this problem, the function is:

[tex]f(x) = x^2 - 2x + 3[/tex]

Hence the coefficients are: [tex]a = 1, b = -2, c = 3[/tex].

Then:

[tex]-\frac{b^2 - 4ac}{4a} = -\frac{(-2)^2 - 4(1)(3)}{4} = 2[/tex]

Hence, the range is [tex](2, \infty)[/tex].

You can learn more about domain and range at https://brainly.com/question/17732416

Otras preguntas