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Let F(x) = 2x2 + x - 3 and g(x) = x - 1. f(x) g(x)
Find and state its domain.

Answers:
1) X - 1; domain is the set of all real numbers
2) (x-1)/(2x + 3) ; domain is the set of all real numbers except-(3/2)
3) 2x + 3; domain is the set of all real numbers except 1​

Respuesta :

Applying the division of functions f(x) and g(x), it is found that the quotient and the domain are given, respectively, by:

3) 2x + 3; domain is the set of all real numbers except 1​.

What is the domain of a function?

It is the set that contains all possible input values.

In this problem, the functions are given as follows:

  • f(x) = 2x² + x - 3.
  • g(x) = x - 1.

Hence the division is given by:

[tex]\frac{f(x)}{g(x)} = \frac{2x^2 + x - 3}{x - 1}[/tex]

The denominator cannot be zero, hence the domain is [tex]x \neq 1[/tex].

Considering that 2x² + x - 3 = (2x + 3)(x - 1), the function can be simplified as 2x + 3, hence option 3 is correct.

More can be learned about the domain of a function at https://brainly.com/question/10891721

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