MHB Compositions and inverse of of functions

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Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

Part B

2) Given the functions f(X) = 7x^2 - 5x and g(x) = 2x - 3 determine and simplify the following:

a) (f-g)(x)

My Answer: 7x^2 - 7x - 3

b) (f - g)(2)

My Answer: 17

c) (fg)(x)

My Answer: 14z^3 - 31x^2 + 5x

d) g^-1(x)

My Answer: 1/2x + 3/2

 

[MarkFL]

Re: Please check my answers - 8

Part a) is incorrect, but it must merely be a typo since you have the correct result for part b). The sign of the third term is wrong.

Part c) is incorrect...you have a typo in which $z$ is where $x$ should be in the first term, and the last term is incorrect, but I suspect this is also a typo.

Part d) is correct.

I don't want to discourage you from posting, and we really do want to help you when you get stuck or need guidance, insights, etc. but for simply checking your results, it may be quicker for you to use a site such as:

Wolfram|Alpha: Computational Knowledge Engine

Many of the problems you posted can be entered there and the answer gotten immediately, to see if your end result is correct. This site can plot functions, find extrema, inverses, simplify expressions, etc.

 

[drop]

Re: Please check my answers - 8

Can you tell me what I did wrong in 3a?

I took f(x) minus g(x) and wrote it like this:
7x^2 - 5x + 0
0x^2 + 2x - 3
7x^2 - 7x - 3

and thank you for that link.

 

[MarkFL]

Re: Please check my answers - 8

Can you tell me what I did wrong in 3a?

I took f(x) minus g(x) and wrote it like this:
7x^2 - 5x + 0
0x^2 + 2x - 3
7x^2 - 7x - 3

and thank you for that link.

I would write:

$$(f-g)(x)=\left(7x^2-5x \right)-\left(2x-3 \right)=7x^2-5x-2x+3=7x^2-7x+3$$

You see, when you subtract, you essentially change all the signs, then add. Subtracting a negative is the same as adding a positive.

Or to use your notation:

7x^2 - 5x + 0
0x^2 + 2x - 3
7x^2 - 7x + 3

 

[drop]

Re: Please check my answers - 8

OH yeah, haha I knew that :P Thanks!

 

[drop]

Re: Please check my answers - 8

Part c) is incorrect...you have a typo in which $z$ is where $x$ should be in the first term, and the last term is incorrect, but I suspect this is also a typo.

Yep, that was a big typo, sorry. Actually what I had written on my paper was:

14x^3 - 31x^2 + 15x

Would that answer be correct?

 

[MarkFL]

Re: Please check my answers - 8

Yep, that was a big typo, sorry. Actually what I had written on my paper was:

14x^3 - 31x^2 + 15x

Would that answer be correct?

Yes, that's correct.