Question

Determine whether the function f(x) = x⁴ - 9 is one-to-one.
1) Yes
2) No

Answer 1

To determine if the function is one-to-one, we compare the values of f(x₁) and f(x₂) and see if they are equal. If they are, the function is not one-to-one. By setting f(x₁) = f(x₂) and solving, we find that x₁ = x₂, hence the function is not one-to-one.

Step-by-step explanation:

To determine whether the function f(x) = x⁴ - 9 is one-to-one, we need to check if every pair of distinct values of x corresponds to distinct values of f(x).

We can do this by setting f(x₁) = f(x₂) and solving for x₁ and x₂. If we find that x₁ = x₂, then the function is not one-to-one.

Let's check:

f(x₁) = x₁⁴ - 9 and f(x₂) = x₂⁴ - 9.

Setting f(x₁) = f(x₂), we have:

x₁⁴ - 9 = x₂⁴ - 9.

Subtracting -9 from both sides:

x₁⁴ = x₂⁴.

Taking the fourth root of both sides:

x₁ = x₂.

Since x₁ = x₂, this means the function is not one-to-one. Therefore, the answer is No.