Given f(x) = x^2 + 4 and g(x) = sqrt (x – 4), what is fog(3)?

Expert Answers
justaguide eNotes educator| Certified Educator

We are given the functions f(x) = x^2 + 4 and g(x) = sqrt(x- 4)

fog(x) = f (g(x)) = f (sqrt (x- 4))

=> (sqrt (x – 4)) ^2 + 4

=> (x – 4) + 4

=> x

Therefore fog (3) = 3.

giorgiana1976 | Student

We'll write the composition of the functions first:

(fog)(x) = f(g(x))

We'll substitute x by g(x):

f(g(x)) = g(x)^2 + 4

f(g(x)) = [sqrt (x – 4)]^2 + 4

f(g(x)) = x - 4 + 4

We'll eliminate like terms:

f(g(x)) = x

So, f(g(3)) = 3.

neela | Student

Given f(x) = x^2 + 4 and g(x) = sqrt (x – 4), To find fog(3).

f(x) = x^2+4.

To find fog(x) we substitute g(x) in place of x in f(x) = x^2+4.

Therefore fog(x) = {sqrt(x-4)}^2+4

fog(x) =x-4+4 = x.

fog(x) = x.

fog(3) = 3.