Question

Given f(x)=√x + 11, find the inverse of f(x). a) f⁻¹(x) = (x + 11)³ b) f⁻¹(x) = x³ - 11 c) f⁻¹(x) = (x - 11)³ d) f⁻¹(x) = x³ + 11

Answer 1

The inverse of the function f(x) = √x + 11 is found by interchanging x and y and solving for y, resulting in f⁻¹(x) = (x - 11)². Therefore, none of the provided options (a-d) is correct.

Step-by-step explanation:

To find the inverse of a function, you interchange the x and y values and then solve for y. This gives you the inverse function.
Let's solve the inverse for the function f(x) = √x + 11.

1. Replace f(x) with y: y = √x + 11
2. Swap x and y: x = √y + 11
3. Solve for y: subtract 11 from both sides to isolate √y: x - 11 = √y
4. Square both sides to eliminate the square root: (x - 11)² = y.

The inverse of f(x) = √x + 11 is f⁻¹(x) = (x - 11)². Therefore, none of the above options is correct.

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