Question

URGENT PLEASE ANSWER 20 POINTS (inverse function)

Answer 1

Explanation:

f(x) = √[ x + 3]; find the inverse function. Here's the procedure:

Replace that "f(x)" with y. Then y = √[ x + 3]

Next, interchange x and y: x = √[ y + 3] => x² = y + 3

Next, solve this latest result for y: y = x² - 3

Finally, replace "y" with the symbol for "inverse of f:"

-1

f (x) = x² - 3

Answer 2

`f^(-1)(x)= x^(2) -3`

Explanation:

To find the inverse of a function, begin by switching the places of the 'y' and 'x' variables. Instead of f(x), we will substitute in 'y' for this purpose.

`f(x) = √(x+3)`

Substitute in 'y':

`y = √(x+3)`

Swap the 'y' and 'x':

`x = √(y+3)`

Square both sides:

`x^(2) = y + 3`

Simplify:

`y = x^(2) -3 \\\\f^(-1)(x) = x^(2) -3`

**Keep in mind, when finding the inverse of a square root function, there is always going to be a restricted domain. In this instance, the restricted domain is
`x\geq 0`