SOLUTION: please explain: If f(x)=4/x and g(x)=3x^5, find (g ∘ f)(x) thank you.

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Question 1140385: please explain:
If f(x)=4/x and g(x)=3x^5, find (g ∘ f)(x)
thank you.
Found 3 solutions by Alan3354, Theo, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
If f(x)=4/x and g(x)=3x^5, find (g ∘ f)(x)
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It's the product.
(4/x)*3x^5

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
f(x) = 4/x
g(x) = 3x^5

(g ∘ f)(x) is the same as g(f(x)).

that's pronounced g of f(x).

here's how it works.

f(x) = 4/x

g(x) = 3x^5

g(f(x)) is equal to g(4/x) which becomes 3 * (4/x) ^ 5

you are replacing the x in g(x) with f(x) which is equal to 4/x.

the result is g(f(x)) = g(4/x) = 3 * (4/x) ^ 5 = 3 * 4^5 / x^5 = 3072 / x^5.

the best way to see how this works is to let x = some random number that's not too big or to small that it becomes unwieldy.

i chose x = 2 because it gives you a clean answer.

you have f(x) = 4/x which becomes f(x) = 4/2 which becomes f(x) = 2.

that's f(x).

g(x) = 3 * x ^ 5

you replace x in g(x) with f(x)) which is equal to 2.

g(f(x)) becomes g(2) which becomes 3 * 2 ^ 5 which becomes 96.

now we previously solved for g(f(x)) in terms of x.

that became g(f(x)) = 3 * (4 / x) ^ 5 which becomes 3072 / x^5.

when x = 2, we get g(f(x)) = 3072 / x^5 which becomes 3072 / 2^5 which becomes 3072 / 32 which becomes 96.

here's a pretty complete reference on composition of functions that you might find informative.

https://www.purplemath.com/modules/fcncomp.htm

if any part of it confuses you, let me know and i'll explain as best i can.

Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website!
.

Alan makes a huge mistake thinking and stating that (g ∘ f)(x) is the product g(x)*f(x).

It is a composition   g ( f(x) ), instead.

And it should be treated as tutor @Theo did it.