Function Operation

[Naz]

Hello,

I have some Functions homework

I am not sure if the question is poorly worded or if I ammisunderstanding the question.

f(x) = √(3x-3) . (Note that this should read the square root of 3x-3, but I couldn't work out how to express it clearly)

g(x) = x+7
Find:
fg(x),gf (x)
I am confused by the comma. Am I just being asked to calculate fg(x) and then gf(x), or does thecomma mean after calculating fg(x) and gf(x) I then have to calculate theirproduct?
I get fg(x) to be √((3x+7)-3), and
gf (x) to be (√(3x-3)) +7
Am I now meant to multiply these two answers together, or isthat it?

Thanks

 

[HallsofIvy]

I don't know of any convention which uses a comma for a product. But it is quite common to use a comma as a short form of "and". "fg(x), gf(x)" asks you to find fg(x) and gf(x) separately.

However, f(g(x)) is NOT \(\displaystyle \sqrt{(3x+ 7)-3}\), it is \(\displaystyle \sqrt{3(x+ 7)- 3}= \sqrt{3x- 18}\). Perhaps the 3 being inside the parentheses was a typo.

 

[Naz]

I don't know of any convention which uses a comma for a product. But it is quite common to use a comma as a short form of "and". "fg(x), gf(x)" asks you to find fg(x) and gf(x) separately.

However, f(g(x)) is NOT \(\displaystyle \sqrt{(3x+ 7)-3}\), it is \(\displaystyle \sqrt{3(x+ 7)- 3}= \sqrt{3x- 18}\). Perhaps the 3 being inside the parentheses was a typo.

Thank you

I did it right on paper but when I came to making my post on here, I made the mistake.

I was coming to the conclusion that the comma was just a separator, but the other questions were so much longer that I thought there was more to it. There weren't any marks to give me a clue

Thanks again for replying. It has reassured me. I looked aroun and couldn't find anything suggesting a comma was an operator, but tend to doubt myself

 

[stapel]

Find: fg(x), gf (x)

As written, these are the products, which may be written out more completely as "(f(x))*(g(x))" and "(g(x))*(f(x))". Was this what you meant, or did you mean (as the other poster guessed) the composition? In other words, did you mean as follows?

. . . . .\(\displaystyle \left(f\, \circ\, g\right)(x)\, \mbox{ and }\, \left(g\, \circ\, f\right)(x)\)

Thank you!

 

[Naz]

As written, these are the products, which may be written out more completely as "(f(x))*(g(x))" and "(g(x))*(f(x))". Was this what you meant, or did you mean (as the other poster guessed) the composition? In other words, did you mean as follows?

. . . . .\(\displaystyle \left(f\, \circ\, g\right)(x)\, \mbox{ and }\, \left(g\, \circ\, f\right)(x)\)

Thank you!

My question was what was meant by the comma in "Find fg(x),gf()"

I thought it might be a mathematical operation like multiply, but I am assuming now that it's just a comma separating the question and it has no more meaning than that