Question

Let f (x) = 4x cos(πx). Show that f (x) is one-to-one?

Answer 1

To show that the function f(x) = 4x cos(πx) is one-to-one, we need to prove that if f(a) = f(b) then a = b. By substituting the values of f(a) and f(b) and solving the equation, we can determine that a must equal b, thus proving that f(x) is one-to-one.

Step-by-step explanation:

To show that the function f(x) = 4x cos(πx) is one-to-one, we need to prove that if f(a) = f(b) then a = b. Let's assume that f(a) = f(b).

Substituting the values of f(a) and f(b), we get:

4a cos(πa) = 4b cos(πb)

Since the value of cos(πx) is always between -1 and 1, we can divide the equation by 4cos(πa) and 4cos(πb), resulting in a = b. Therefore, f(x) is one-to-one.