please help, how do i do this one: f(x) = x^2 + 3; g(x) = Square root of quantity x minus two.

Find f(g(x)).

Question

please help, how do i do this one: f(x) = x^2 + 3; g(x) = Square root of quantity x minus two.

Find f(g(x)).

zyberg · Answer

Well, think about it analytically: f(g(x)) means what? That the x in f(x) will be the solution of function g(x). Can you figure out the problem now?

iwanttogotostanford · Answer

no, how would i go about solving it I still don't know. How do you do these types of problems?

zyberg · Answer

Well, what I said would mean that f(g(x)) is the same as f(Square root of quantity x minus two). Can you get it now?

iwanttogotostanford · Answer

so would it be squareroot x^2+3 ?

zyberg · Answer

No no no! You just need to substitute "Square root of quantity x minus two" as x in the f(x) function.

zyberg · Answer

$$\sqrt{x - 2}$$ is the x in the f(x) function, if you have f(g(x))

iwanttogotostanford · Answer

ok so now I have f(x)= square x-2 ^2 + 3

zyberg · Answer

Yes ;) I am not sure, if you meant to take the root of whole expression ($$\sqrt{x-2}$$) or just x, but depending on that, you square it (you get either x - 2 or -x + 2 (if the root is of both elements) or x + 4, if the root was only on x).

iwanttogotostanford · Answer

so my answer would just be: f(g)(x))= square root of x^2+3 ? OR would it be something else? There are 3 other different options

er.mohd.amir · Answer

put value of g(x)  in place of x in f(x) and simplifying it

zyberg · Answer

@iwanttogotostanford You are missing the + 2 part ;) and how long is the square root going for?

iwanttogotostanford · Answer

ok well then now I have square x-2 = x^2+3 and I don't know how to exactly simplify that

iwanttogotostanford · Answer

and the square root is going on most of it

zyberg · Answer

$$f(g(x))= x + 7$$

iwanttogotostanford · Answer

how'd you get that...

iwanttogotostanford · Answer

btw here are my answer choices just for reference: 
 f(g(x)) = (x2 + 3)(Square root of quantity x minus two.)
 f(g(x)) = Square root of quantity x minus two divided by quantity x squared plus three.
 f(g(x)) = x + 1
 f(g(x)) = Square root of quantity x squared plus three.

zyberg · Answer

Sorry! My answer is wrong! $$f(g(x))= (\sqrt{x}-2)^{2}+3$$ $$(\sqrt{x}-2)^{2}+3 = x - 4\sqrt{x} + 7$$

zyberg · Answer

I think, that I might have misunderstood your problem ;) Could you write original problem with proper formating? (you can use "Equation" tab just below the chat box).

zyberg · Answer

Or, look: $$f(g(x))= g(x)^{2} + 3$$

iwanttogotostanford · Answer

ok i will

iwanttogotostanford · Answer

$$f(x)=x^2+3 ; g(x)=\sqrt{x-2}    $$   Find f(g)(x))

iwanttogotostanford · Answer

that was my problem^

zyberg · Answer

$$f(g(x))=g(x)^{2}; f(g(x))= (\sqrt{x-2})^{2}+3$$ Can you solve this?

iwanttogotostanford · Answer

no, that looks harder than my original problem...

iwanttogotostanford · Answer

would it just be g(x)^2 = (square root x-2)^2 + 3 ?

zyberg · Answer

$$(\sqrt{x-2})^{2} + 3 $$ is the answer, however, you can simplify it.

zyberg · Answer

It has two answers, since square root is a modulus operation. $$(\sqrt{x-2})^{2}$$ is either  x - 2 or x + 2. 
Answer #1 when $$x \ge2; x + 1$$ 
Answer #2 when $$x < 2; 5 - x$$

zyberg · Answer

(I gave you the answers for the whole function, with + 3 at the end)

iwanttogotostanford · Answer

i still don't quite understand how you got it, but thank you! I sort of get it.

iwanttogotostanford · Answer

wait never mind... i get i!!!

iwanttogotostanford · Answer

i reviewed what you said and it makes sense to me now. thank yoU!

zyberg · Answer

No problem, I just did this: $$g(x)^2 + 3 = f(g(x)); since f(x)= x^2 + 3$$

iwanttogotostanford · Answer

thanks!