Question

Find (f∘g)(4) for the following functions. Round your answer to two decimal places, if necessary. f(x)=√x+1 and g(x)=3+√x

Answer 1

2.45

Explanation:

Given f(x)=√x+1 and g(x)=3+√x, to calculate for (f∘g)(4), first we need to get the function (f∘g)(x).

(f∘g)(x). = f{g(x)}

since g(x) =3+√x, then;

f{g(x)} = f(3+√x)

If f(x) = √x+1

f(3+√x) can be gotten by simply replacing x with 3+√x in f(x)

f(3+√x) = √(3+√x)+1

f{g(x)} = √(3+√x)+1

f{g(4)} can be gotten by substituting x = 4 into the resulting function above.

f{g(4)} = √(3+√4)+1

f{g(4)} = √(3+2)+1

f{g(4)} = √5+1

f{g(4)} = √6

f{g(4)} = 2.449 ≈ 2.45 to two decimal places.

Hence, (f∘g)(4) for the functions to two decimal places is 2.45