help help!~@!!!?

Question

The inverse of the function f(x)= (x + 3)2 is...??

and what is the reason?

why is this a function?

Answer 1

inverse is y = (x/5) oops (1/2)x -3

y=(x+3)2
(y/2)=x+3
(X/2)=y+3 (switch x and y)
-y= (-x/2)+3
y=(x/2)-3
y = (1/2)x-3

easiest way to proof is to add values to x for regular and inverse to see if its correct.
if you put 6 into the original, you get 18
if you put 18 in the inverse, you get 6

if you have a graphing calc also, you can have both lines drawn and then do a y=x line to see if they are spaced apart evenly but this is harder to tell on most graphing calcs due to their dimensions

IF f(x)= (x + 3)2 is supposed to mean f(x)= (x + 3)^2, then the lady below has ya covered "y = +-[sqrt(x)]-3"

Answer 2

You just switch everything. That's why it's called the inverse, it's quite easy. So it changes to x-3 over 2 (which is the same as dividing)

Answer 3

let g be the inverse of f. Then
f(g(x))=x or g(f(x))=x

to construct the inverse of a function y = f(x), solve for x, then exchange the variables.

y=f(x)=(x+3)2
y=2x+6
2x=y-6
x=(y-6)/2...............solved for x

y=(x-6)/2 .....................variables interchanged.
Here y is inverse of f(x) i.e., g(x)
g(x)=(x-6)/2

Inverse of (x+3)2 is (x-6)/2

Answer 4

f(x)= (x + 3)^2
let
y = (x + 3)^2
x+3 =√y
x = √y - 3
f^ (-1)(x) =(√x) - 3#

Answer 5

f(x) is same thing as y.

Therefore,
y=2x+6

inverse is y=1/2x+6