Question

Which of the following is the inverse of f(x) = 3-x⁵?

1) ƒ˜¹(x) = 3 - x⁵
2) f-1(x) = 5² – 3
3) f-1(x) = 5² - 3
4) Æ’-1(x) = 3 – 5²

Answer 1

To find the inverse of f(x) = 3 - x^5, we swap x and f(x), subtract 3 from both sides, multiply by -1, and take the fifth root. The correct inverse function is f^-1(x) = (3 - x)^(1/5), but this option is not provided.

Step-by-step explanation:

The question is asking to identify the inverse function of f(x) = 3 - x5. To find the inverse function, we typically swap the 'x' and 'y' (or 'f(x)') and solve for 'y'. The original equation f(x) is rewritten as x = 3 - y5. To solve for 'y', we follow these steps:

1. Subtract 3 from both sides: x - 3 = -y5.
2. Multiply by -1 to get rid of the negative sign: 3 - x = y5.
3. Take the fifth root of both sides to solve for 'y': y = (3 - x)1/5 or y = √5(3 - x).

Therefore, the inverse function is f-1(x) = √5(3 - x), which is not explicitly listed in the options provided. However, since none of the provided options is technically correct, this would need to be communicated to the student.