Question 1106851: Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y = three divided by square root of quantity three x plus four.
y= 3/sqrt(3x+4)
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
Think of how you would evaluate the expression for a particular value of x:
(1) multiply by 3
(2) add 4
(3) take the square root
(4) divide 3 by the result
To write the whole expression as a composition of two functions, you can break the steps into two parts any way you want.
solution #1:
g(x) = multiply by 3 and add 4;
f(x) = take the square root and divide 3 by the result
answer #1: g(x) = 3x+4; f(x) = 3/sqrt(x)
solution #2:
g(x) = multiply by 3, add 4, and take the square root
f(x) = divided 3 by the result
answer #2: g(x) = sqrt(3x+4); f(x) = 3/x
solution #3:
g(x) = multiply by 3
f(x) = add 4, take the square root, and divide 3 by the result
answer #3: g(x) = 3x; f(x) = 3/sqrt(x+4)
Solution #4: You could even do something like this, combining all the steps into one of the functions -- although I don't see that it would ever be useful:
g(x) = 3/sqrt(3x+4); f(x) = x
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