Question

For ​f(x)=\sqrt(x) and ​g(x)=x-3​, find (fog)(x), (gof)(x), (fog)(7), (gof)(7)

Answer 1

The compositions are:

(fog)(x) =√(x - 3)

(gof)(x) = √x - 3

(fog)(7) = 2

(gof)(7) = -0.35

Let's find the compositions.

Remember that (fog)(x) = f(g(x))

Here we have the functions:

f(x) = √x

g(x) = x - 3

Then:

(fog)(x) = f(g(x)) = √g(x) = √(x - 3)

(gof)(x) = g(f(x)) = f(x) - 3 = √x - 3

Now let's evaluate these, we will have:

(fog)(7) = √(7 - 3) = 2

(gof)(7) =√7 - 3 = -0.35