Question

For the function f(x) = √x - 3, find f^(-1)(x). a) f^(-1)(x) = (x+3) b) f^(-1)(x) = x + 3 c) f^(-1)(x) = 7x + 3 d) f^(-1)(x) = √(x + 3)

Answer 1

The inverse function f^(-1)(x) is f^(-1)(x) = x^2 + 6x + 9.

None of the option is true.

Explanation:

To find the inverse of the function f(x) = √x - 3, denoted as f^(-1)(x), we need to swap the roles of x and y and then solve for y.

Let's start by swapping x and y:

x = √y - 3

Next, we'll isolate the square root term:

x + 3 = √y

To eliminate the square root, we square both sides of the equation:

(x + 3)^2 = (√y)^2

Simplifying:

x^2 + 6x + 9 = y

Now, we have expressed y in terms of x, which is the inverse function of f(x).

So, the inverse function f^(-1)(x) is:

f^(-1)(x) = x^2 + 6x + 9

Therefore,

The inverse function f^(-1)(x) is f^(-1)(x) = x^2 + 6x + 9.

None of the option is true.