Question

Function notation question. Please help!

Answer 1

Go ahead

Answer 2

Given : \[f(x)=\sqrt{4-x^2}\] & \[g(x)=\sqrt{1+x}\]
Find : \[f+g(\sqrt{2})\]

Answer 3

Is it \(f\circ g(\sqrt{2})\)?

Answer 4

There is an addition symbol so I don 't think so.

Answer 5

\[(f+g)(\sqrt{2})\] like that right...

Answer 6

I guess so...

Answer 7

So, what's your attempt?

Answer 8

Would be easier to do \[(f+g)(x) \] first then \[(f+g)(\sqrt{2})\]

Answer 9

Ok, that makes more sense, I'll let batman take it

Answer 10

Ah, sorry to intrude Fibonacci, but you can take it away if you like :)

Answer 11

Well, I inserted f and g into the equation. But, since there were no parenthesis around f+g, i multiplied the square root of 2 by the square root 1+x to get the square root of 2+2x

Answer 12

It's probably not right, I'm really confused.

Answer 13

Well, what is it asking you for? it's asking for f+g, so what is f+g in terms of x?

Answer 14

like if you have two recipes, recipe f and recipe g, and you add the ingredients together to make one total recipe

Answer 15

what do you do?

Answer 16

I 'm not sure...

Answer 17

Ah so your question is asking, f(x)+g(2^1/2) basically, it's just hard to know what exactly you're asking unless you take a picture of the question itself and post it.

Answer 18

\[f(x)+g(x) = (f+g)(x)\]

Answer 19

You can see you're just factoring out the x.

Answer 20

that's what I'm interpreting it as batman

Answer 21

I'm just trying to think of a real world isomorphism

Answer 22

Yeah it doesn't make much sense though without parenthesis

Answer 23

I'll get a picture, two sec.

Answer 24

Np, :)

Answer 25

cooleos

Answer 26

It's the question to the left.

Answer 27

that is a poorly written question...

Answer 28

but I think batman's interpretation should be fine

Answer 29

Tell my math teacher that. XD

Answer 30

gladly

Answer 31

Yeah it's asking (f+g)(2^1/2) otherwise it's written wrongly.

Answer 32

So how do I attempt it?

Answer 33

So as I mentioned before find \[(f+g)(x) \] first meaning, add the two equations.

Answer 34

so have you ever baked, gotten two separate checks or something similar?

Answer 35

Yes.

Answer 36

\[f(x)=\sqrt{4-x^2} ~~~g(x) = \sqrt{1+x} ~~~ (f+g)(x) \implies (\sqrt{4-x^2})+(\sqrt{1+x})\]

Answer 37

Well you can't really do much I suppose so just skip to \[(f+g)(\sqrt{2})\]

Answer 38

so, if you bake and you want to double your recipe or add two recipes together, what do you do?

Answer 39

(I'm just explaining concept, batman's is the math speak)

Answer 40

Haha, well \[(f+g)(\sqrt{2}) \implies (\sqrt{4-\sqrt{2}^2})+(\sqrt{1+\sqrt{2}})\]

Answer 41

This is how I originally attempted it. I then assumed that I could use the quadratic formula. I'm guessing this is wrong ? @iambatman @fibonaccichick666

Answer 42

ahhh ok so example: if we have h(x)=x^2 then h(2)=2^2 DO YOU SEE?

Answer 43

sorry for caps hit the caps lock key

Answer 44

Yes, I see.

Answer 45

So would that be right ?

Answer 46

no, not quite

Answer 47

Ah, I see.

Answer 48

so I think the issue is notation that was not explained properly, Your intuition was great to just multiply the two, but you want to substitute the number for all of the x's

Answer 49

I plug in the square root of 2 for x

Answer 50

YES! :)

technically... as written, you are correct and could argue that that is what the teacher asked you to do, but I don't recommend it

Answer 51

although you wouldn't square it as you did

Answer 52

Yeah, would you mind guiding me through the rest. I 'm really bad with radicals...

Answer 53

well to start, just tell me what (f+g)[of](x)=?

I added the of because that is how you would say it, it doesn't get written that way. Also are you better with exponents?

Answer 54

Yes, I'm pretty good\[\sqrt{4-(\sqrt{2})^2}+\sqrt{1+(\sqrt{2})}\] with exponents.

Answer 55

Try simplifying it

Answer 56

so first, that is (f+g)(√2), second, a square root is just the exponent 1/2

Answer 57

\[\sqrt{2}^2\] like what does this mean? :P

Answer 58

\[\sqrt{2}+\sqrt{1+\sqrt{2}}\]

Answer 59

Yeah, that's good.

Answer 60

That's your final answer

Answer 61

Really ?

Answer 62

yup

Answer 63

Yeah unless you have a calculator

Answer 64

I do.

Answer 65

then you can get a numeric answer, however, it will not be exact

Answer 66

I think I'm supposed to leave it like this so thanks for the help you guys.

Answer 67

Np :)

Answer 68

np :)

Answer 69

Now, make sure you tell your teacher that they missed a vital thing in the question. Those parentheses are really important for meaning in the question ;P

Answer 70

Will do.

Answer 71

Hey this was troubling me, and I looked into it, I guess I haven't done this in a while but the notation is fine, but it does imply what we did, so if you have \[f-g(x) \] it's the same thing as \[(f-g)(x)\] thought I'd get that straight. :)

Answer 72

thanks, I'd never seen it written that way before either