Question

could anyone help me?!? :D

find the inverse function of g(x)=x^2+2x+3 when x is greater than or equal to -1.

Answer 1

are you able to complete the square for that quadratic?

Answer 2

is there a way to solve it without completing the square? cuz i dont really remember how to do that haha...been a long summer...

Answer 3

no not that I can see

Answer 4

oh could u refresh me on how to do it then ? :/

Answer 5

focus on x^2+2x

Answer 6

what term is missing to make that a perfect square?

Answer 7

+1?

Answer 8

x^2+2x+1?

Answer 9

:(

Answer 10

yes that is correct

Answer 11

so if we had x^2 + 2x + 1, we could factor that to (x+1)^2

Answer 12

however, we have x^2+2x+3

Answer 13

one thing we can do is break up that 3 into 1+2

so we now have x^2+2x+1+2

Answer 14

then we factor x^2 + 2x + 1 to get (x+1)^2

so we now have

g(x) = (x+1)^2 + 2

Answer 15

making sense?

Answer 16

yes so far

Answer 17

so we have y = (x+1)^2 + 2

Answer 18

how do we find the inverse of that?

Answer 19

change y and x and solve for y again?

Answer 20

correct

Answer 21

so solve for y in x = (y+1)^2 + 2

Answer 22

\[y=+/- \sqrt{x-2}-1\]

Answer 23

ok, so why was the domain restricted to begin with?

Answer 24

or

\[\Large y=-1 \pm \sqrt{x-2}\]

but you pretty much got it. There's one slight issue though

Answer 25

let's look at a rough graph of y = x^2+2x+3

Answer 26

That is the same as y = (x+1)^2 + 2

so we see that the vertex is (-1,2) since that equation above is in vertex form y = a(x-h)^2 + k

Answer 27

Rough Sketch of y = x^2+2x+3 or y = (x+1)^2 + 2