Question

Let f(x) = (2x-3)/(x+1). Which of the following statements are true?

1) The function f(x) is defined for all real numbers.
2) The function f(x) is undefined at x = -1.
3) The function f(x) is a linear function.
4) The function f(x) is a quadratic function.

Answer 1

The function f(x) = (2x-3)/(x+1) is undefined at x = -1. It is not a linear function and also not a quadratic function.

Step-by-step explanation:

The function f(x) = (2x-3)/(x+1) is defined for all real numbers except when the denominator (x+1) equals zero. So, the function is undefined at x = -1. Therefore, statement 2) The function f(x) is undefined at x = -1 is true.

Since f(x) is a rational function with a degree of 1 in the numerator and denominator, it is not a linear function. Therefore, statement 3) The function f(x) is a linear function is false.

The function f(x) = (2x-3)/(x+1) is a rational function, not a quadratic function. Therefore, statement 4) The function f(x) is a quadratic function is false.