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Hi there, I need help with composition of functions.

I need to find fog, gof, gog, and fof and their domains for the following:

f(x) = square root of 2x +3
g(x) = x^2 + 1

if someone can help me asap that would be so great!

  • Calculus -

    For g of f, substitute sqrt(2x +3) for x in g(x)

    You get (2x + 3) + 1 = 2x + 4

    The domain is all numbers in thnis case.

    Do the others the same way. We will gladly critique your work.

  • Calculus -

    okay, so i tried out subtsting x into f (x) and i got sqrt (2x^2 +5) that right?

    and what do u mean domain is all in numbers?

    can u help me with the f o f and g og?

    and a side question, we got a table of values that was something like
    x 1 2 3 4 5 6
    f(x) 3 1 .....
    g(x) 6

    so the first question is like evaulaute:
    would that be

  • Calculus -

    Are you trying to calculate f of g(x)?

    Assuming f(x) = sqrt(2x+3) and not sqrt (2x) + 3, f of g(x) would be
    sqrt [2(x^2 +1) + 3]= sqrt (2x^2 + 5)
    So you would be correct.

    g of g(x) = (x^2+1)^2 +1 = x^2 + 2x + 2

    To your side question: yes, the first answer is 18.

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