Question

Is f (x) = x^2 + 1 a one-to-one function? Explain

A. Yes, the inverse of f(x) is a function
B. Yes, the inverse of f(x) is not a function
C. No; the inverse of f(x) is a function,
D. No, the inverse of f(x) is not a function

Answer 1

The function f(x) = x^2 + 1 is not a one-to-one function because different x-values can produce the same y-value. This violates the criteria of a one-to-one function where each y-value must be paired with exactly one x-value.

Step-by-step explanation:

The function f(x) = x^2 + 1 is not a one-to-one function. To determine if a function is one-to-one, we check if every y-value is paired with exactly one x-value. In the case of f(x) = x^2 + 1, if we input both a positive and a negative value for x that have the same magnitude, they will yield the same y-value. For example, f(2) = 2^2 + 1 = 5 and f(-2) = (-2)^2 + 1 = 5. This means that the function is not one-to-one, because the y-value of 5 corresponds to two different x-values: 2 and -2.

No, the function f(x) = x^2 + 1 is not one-to-one. In order for a function to be one-to-one, each input value (x) must produce a unique output value (y). However, in this case, different input values can produce the same output. For example, f(1) = 1^2 + 1 = 2 and f(-1) = (-1)^2 + 1 = 2, which means two different input values (1 and -1) produce the same output (2). This violates the definition of a one-to-one function.