pre calculus

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1.) If h(x)= (fog)(x) and h(x) = 3 over the square root of x+3 , find g(x) if f(x)= 3 over the square root of x+2.

my answer is x+1. Am I right?

2.)If f(x)=3x,g(x)=x-3,and h(x)= the square root of x, find (fogox)(X). I really didn't get this will someone please show me how to do it?

  • pre calculus -

    The first one is correct but I am still not sure about the second one.
    This I what I did to solve for it:
    3(x-3)
    3(he square root of 25-3
    3(5-3)
    15-9=6

    Is it correct?

  • pre calculus -

    f(x) = 3/√(x+2)
    f(g) = 3/√(g+2) = 3/√(x+3)
    so, you are correct; g(x) = x+1

    for the second one, you're not solving any equation; you're just expressing a composite function as a single one, just as in #1.

    f(x) = 3x
    g(x) = x-3
    h(x) = √x

    (f◦g◦h)(x) = f(g(h(x)))
    f(g(h)) = f(h-3) = 3(h-3) = 3(√x-3)
    or,
    f(g(h)) = 3(g(h)) = 3(g(√x)) = 3(√x-3)

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