Is f(x)=4x2−3 a one-to-one function on the domain (−∞,∞)?
Options:
-No, f(x)=4x2−3 is not a one-to-one function on (−∞,∞) because there is an output value that has more than one corresponding input value.
-Yes, f(x)=4x2−3 is a one-to-one function on (−∞,∞) because there is an output value that has more than one corresponding input value.
-Yes, f(x)=4x2−3 is a one-to-one function on (−∞,∞) because each output value has exactly one input value.
To determine if the function f(x) = 4x^2 - 3 is a one-to-one function on the domain (-∞, ∞), we need to consider the concept of one-to-one functions.
A function is said to be one-to-one if each output value (y-coordinate) corresponds to exactly one unique input value (x-coordinate), and vice versa. In other words, if two different input values give the same output value, the function is not one-to-one.
For the given function f(x) = 4x^2 - 3, we can observe that for each input value x, we will have a unique output value y. No two different input values will give the same output value. Therefore, each output value has exactly one corresponding input value, making the function one-to-one.
So, the correct option is:
-Yes, f(x) = 4x^2 - 3 is a one-to-one function on (-∞, ∞) because each output value has exactly one input value.