Posted by Leo on Saturday, April 6, 2013 at 5:50pm.
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)=x3,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  Leo, Saturday, April 6, 2013 at 6:34pm
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(x3)
3(he square root of 253
3(53)
159=6
Is it correct?

pre calculus  Steve, Sunday, April 7, 2013 at 6:30am
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) = x3
h(x) = √x
(f◦g◦h)(x) = f(g(h(x)))
f(g(h)) = f(h3) = 3(h3) = 3(√x3)
or,
f(g(h)) = 3(g(h)) = 3(g(√x)) = 3(√x3)
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