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Question 1141914: Calculus Question

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

The given function performs 4 operations on the input value:
(1) square it;
(2) subtract 1;
(3) take the square root; and
(4) add 2

So you could write the function as the composition of 4 functions:
p(x) = x^2
q(x) = x-1
r(x) = sqrt(x)
s(x) = x+2

s(r(q(p(x)))) = s(r(q(x^2))) = s(r(x^2-1)) = s(sqrt(x^2-1)) = sqrt(x^2-1)+2

If you need to write the function as the composition of 3 functions, none of which is the identity, simply combine two of the four operations into one. So one possible answer is
h(x) = x^2
g(x) = sqrt(x-1)
f(x) = x+2

Then

f(g(h(x))) = f(g(x^2)) = f(sqrt(x^2-1) = sqrt(x^2-1)+2

There are of course other possible answers....

SOLUTION: Calculus Question <img src="https://drive.google.com/uc?id=14PN3_HnOTVuQkYJpEOuz3t11haT7shXh">