Question

URGENT PLEASE ANSWER 20 POINTS (inverse function)

Answer 1

Answer:

$f^{-1}(x)= x^{2} -3$  

Step-by-step 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.

$f(x) = \sqrt{x+3}$

Substitute in 'y':

$y = \sqrt{x+3}$

Swap the 'y' and 'x':

$x = \sqrt{y+3}$

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  $x\geq 0$

Answer 2

Answer:

Step-by-step 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