add, mult, div, sub functions

[marshall1432]

Can someone healp me get the solutions? I have worked out the way i think thay are so a little help would be great!

1. Let f(x) = x + 2 and g(x) = 1/(x + 3). Find (f + g)(x).

My solution: f(g(x))=1/(x+3) sub x in for the g(x) function
f(x)=1/(x+3)+2 sub 1/(x+3) in for the x function

Answer: 1/(x+5)

2. Let f(x) = 5x^2 + -4 and g(x) = 4x. Find (f o g)(2).

My Solution: f(g(2))=4(2)=8 sub in 2 for the g(x) function
5(8)^2+-4 sub in 8 for the f(x) function

Answer: 316

3. Let f(x) = 2x2 - 1 and g(x) = x + 3. Find the function (g o f)(x).

My Solution: g(f(x))=2x2-1 sub x in for the f(x) function
2x2-1+3 sub 2x2-1+3 in for the g(x) function

Here is where I am stumped. the answer I got was 2x2+2. I need to simplify the answer and get an "x" value.

4. Let f(x) = 3x + 1 and g(x) = (x - 4)/3. Find the function (f o g)(x).

My Solution: f(g(x))=(x-4)/3
3(x-4)/3+1

Answer: 3x-12/3+1
x-4/4

Any help??

5. Find functions f(x) and g(x) such that (f o g)(x) = 1/(x + 2).

I don't know how to set this one up.

I hope I provided enough information for someone to help me get these resolved. Thanks

 

[skeeter]

Can someone healp me get the solutions? I have worked out the way i think thay are so a little help would be great!

1. Let f(x) = x + 2 and g(x) = 1/(x + 3). Find (f + g)(x).

My solution: f(g(x))=1/(x+3) sub x in for the g(x) function
f(x)=1/(x+3)+2 sub 1/(x+3) in for the x function

Answer: 1/(x+5)

no ...
(f+g)(x) = f(x) + g(x) = (x + 2) + 1/(x + 3) = (x² + 5x + 7)/(x + 3)

2. Let f(x) = 5x^2 + -4 and g(x) = 4x. Find (f o g)(2).

My Solution: f(g(2))=4(2)=8 sub in 2 for the g(x) function
5(8)^2+-4 sub in 8 for the f(x) function

Answer: 316 correct

3. Let f(x) = 2x2 - 1 and g(x) = x + 3. Find the function (g o f)(x).

My Solution: g(f(x))=2x2-1 sub x in for the f(x) function
2x2-1+3 sub 2x2-1+3 in for the g(x) function

Here is where I am stumped. the answer I got was 2x2+2. I need to simplify the answer and get an "x" value.

the "answer" is simplified as much as is needed ... you coluld factor out a 2, but that's about it. the function g[f(x)] = (2x² - 1) + 3 = 2x² + 2 = 2(x² + 1)

4. Let f(x) = 3x + 1 and g(x) = (x - 4)/3. Find the function (f o g)(x).

My Solution: f(g(x))=(x-4)/3
3(x-4)/3+1

Answer: 3x-12/3+1
x-4/4

no ...
f[g(x)] = 3[(x - 4)/3] + 1 = (x - 4) + 1 = x - 3

Any help??

5. Find functions f(x) and g(x) such that (f o g)(x) = 1/(x + 2).

let's keep it simple ... how about g(x) = x + 2 and f(x) = 1/x ???

I don't know how to set this one up.

I hope I provided enough information for someone to help me get these resolved. Thanks

 

[marshall1432]

gosh, i feel like an idiot on 1 and 3, i knew those and i guess i was in a rush when i worked them out. i do have ?'s about 4 and 5 though.

4. Let f(x) = 3x + 1 and g(x) = (x - 4)/3. Find the function (f o g)(x).

f[g(x)] = 3[(x - 4)/3] + 1 = (x - 4) + 1 = x - 3

Then do I take x-3 and insert it in for f(x) and get 3(x-3)+1?

5. Find functions f(x) and g(x) such that (f o g)(x) = 1/(x + 2).

g(x) = x + 2 and f(x) = 1/x ???

Then what do I do after that?

Thanks

 

[Mrspi]

Can someone healp me get the solutions? I have worked out the way i think thay are so a little help would be great!

1. Let f(x) = x + 2 and g(x) = 1/(x + 3). Find (f + g)(x).

My solution: f(g(x))=1/(x+3) sub x in for the g(x) function
f(x)=1/(x+3)+2 sub 1/(x+3) in for the x function

Answer: 1/(x+5)<-----incorrect
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (x + 2) + [1 / (x + 3)]
Now, you need to combine the two. (x + 2) is the same thing as (x + 2)/1. Write that as a fraction with (x + 3) as its denominator: (x + 2)(x + 3)/(x + 3)

(f + g)(x) = [(x + 2)(x + 3)/(x + 3)] + [1/(x + 3)]
(f + g)(x) = [(x + 2)(x + 3) + 1]/(x + 3)
(f + g)(x) = (x² + 5x + 6 + 1)/(x + 3)
(f + g)(x) = (x<SUP>2</SUP> + 5x + 7) / (x + 3)

2. Let f(x) = 5x^2 + -4 and g(x) = 4x. Find (f o g)(2).

My Solution: f(g(2))=4(2)=8 sub in 2 for the g(x) function
5(8)^2+-4 sub in 8 for the f(x) function

Answer: 316<-----looks ok

3. Let f(x) = 2x2 - 1 and g(x) = x + 3. Find the function (g o f)(x).

My Solution: g(f(x))=2x2-1 sub x in for the f(x) function
2x2-1+3 sub 2x2-1+3 in for the g(x) function
I find your "explanation" hard to follow.
f(x) = 2x<SUP>2</SUP> - 1
so, (g o f)(x) = g(2x<SUP>2</SUP> - 1)
you will substitute (2x<SUP>2</SUP> - 1) for x in the "g function rule"
g(2x<SUP>2</SUP> - 1) = (2x<SUP>2</SUP> - 1) + 3


Here is where I am stumped. the answer I got was 2x2+2. I need to simplify the answer and get an "x" value.<----no, you don't necessarily end up with an "x" value. You aren't looking for x! You are looking for (f o g)(x), and you found it:

(f o g)(x) = 2x<SUP>2</SUP> + 2


4. Let f(x) = 3x + 1 and g(x) = (x - 4)/3. Find the function (f o g)(x).

My Solution: f(g(x))=(x-4)/3
3(x-4)/3+1

Answer: 3x-12/3+1
x-4/4<-----incorrect

You set it up correctly....but maybe some grouping symbols would be a good idea:

f(g(x)) = 3*[(x - 4) / 3] + 1
You've got to do the multiplication first. 3*[(x - 4) / 3] is just x - 4!
f(g(x)) = x - 4 + 1
f(g(x)) = x - 3


Any help??

I hope I provided enough information for someone to help me get these resolved. Thanks

 

[marshall1432]

Okay; I understand the first three problems now. Thank you!

On problem (4), do I simply insert "x - 3" in for f(x) and get 3(x - 3) + 1?

On problem (5), what do I do?

 

[stapel]

4) Let f(x) = 3x + 1 and g(x) = (x - 4)/3. Find the function (f o g)(x).

Plug the formula for g(x) in for "x" in the formula for f(x). Then simplify.

5) Find functions f(x) and g(x) such that (f o g)(x) = 1/(x + 2).

Use your imagination. (There is probably more than one right answer.) What is the "first" thing you see being done to x? Make that the formula for g(x). What is the "second" thing you see being done to "x"? Make that the formula for f(x).

Then test your formulas by doing the compositon yourself.

Note: Until you understand how to do exercises (2) through (4), you will probably not have much luck with (5). But giving you an answer wouldn't help you on the test at all, so keep working until you "get" the first four exercises. Then try (5).

Eliz.

 

[marshall1432]

i know i must have said it 5 times now but isnt 4: 3(x-4)/3+1?
answer: 3x-12/3+1
3x-4+1
3x-5?

 

[skeeter]

Okay; I understand the first three problems now. Thank you!

On problem (4), do I simply insert "x - 3" in for f(x) and get 3(x - 3) + 1?

no ... you're done f[g(x)] = x-3 ... that's all.

On problem (5), what do I do?

nothing again, all they asked for is two functions, f and g, whose composition is 1/(x+1) ... I gave you a simple pair of functions that work

f(x) = 1/x, and g(x) = x + 1 ...

f[g(x)] = f(x+1) = 1/(x+1)

 

[stapel]

i know i must have said it 5 times now but isnt 4: 3(x-4)/3+1?
answer: 3x-12/3+1
3x-4+1
3x-5?

Actually, you've only shown work on this exercise twice, giving different answers each time.

Perhaps it might help if you read the tutors' replies in full, since you have been given completely worked answers...? (I reiterated the steps necessary, assuming you weren't quite clear on how the tutors had arrived at the solutions they'd given you. I apologize if some misunderstanding on my part has caused you offense.)

Thank you.

Eliz.