I've done it before with ease (about 6 months ago) so I know it's not that hard, but my text book doesn't explain it very well, and I know (f ∘ g) is the same as [f(g(x))] but it's not registering how to solve...For example, Given: f(x) = √2x-3 and g(x) = x^2 - 2Find: (f ∘ g)(4)What's the input? g? Do I replace the x in f(x) with g? Thanks for any help :). Created by Ashley. science-mathematics-en - mathematics-en

Will someone explain how the composition of functions (f ∘ g) works?

May 2021 2 68 Report

Will someone explain how the composition of functions (f ∘ g) works?

I've done it before with ease (about 6 months ago) so I know it's not that hard, but my text book doesn't explain it very well, and I know (f ∘ g) is the same as [f(g(x))] but it's not registering how to solve...

For example,

Given: f(x) = √2x-3 and g(x) = x^2 - 2

Find: (f ∘ g)(4)

What's the input? g? Do I replace the x in f(x) with g?

Thanks for any help :)

Science & Mathematics / Mathematics

cutesexyangelbabe

Verified answer

Yes, you can either first substitute g(x) for x in f(x), and then evaluate the new function (f ∘ g)(x) at 4, or you can find g(4) and substitute this value for x in f(x).

I'm not sure if this is what you have, but assuming your f(x) = sqrt(2x - 3):

Using the first method, (f ∘ g)(x) = sqrt(2*(x^2 - 2) - 3) = sqrt(2x^2 - 4 - 3) = sqrt(2x^2 - 7).

So (f ∘ g)(4) = sqrt(2(4)^2- 7) = sqrt(32 - 7) = sqrt(25) = 5.

Using the second method, g(4) = (4)^2 - 2 = 14.

Then f(14) = sqrt(2(14) - 3) = sqrt(25) = 5. This agrees with the first method.