Find functions f and g such that (f o g)(x) = √(2x) + 19

Question

Find functions f and g such that (f o g)(x) =
`√(2x) + 19`

Answer 1

We have the expression:

`(fog)(x)=\sqrt[]{2x}+19`

So:

`g(x)=2x`
`f(x)=\sqrt[]{x}+19`

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Since we want to get the function g composed in the function f, and the result of this is:

`(fog)(x)=\sqrt[]{2x}+19`

When we replace g in f, we have to get as answer the previous expression. And by looking at it the only place where we will be able to replace values is where the variable x is located. The function f will have the "skeleton" or shape of the overall function and g will be injected in it.

From this, we can have that f might be x + 19 and g might be sqrt(2x), but the only options that are given such that when we replace g in x of f, are f = sqrt(x) + 19 and g = 2x.