SOLUTION: Provided f(x) = √x+2 (under whole squareroot) and g(x) = x / x + 1 Find (f ◦ g)(3) and (g ◦ f)(3).

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Provided f(x) = √x+2 (under whole squareroot) and g(x) = x / x + 1 Find (f ◦ g)(3) and (g ◦ f)(3).      Log On


   

Question 1133183: Provided f(x) = √x+2 (under whole squareroot) and g(x) = x / x + 1
Find (f ◦ g)(3) and (g ◦ f)(3).
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Provided
f%28x%29+=+sqrt%28x%2B2%29+
g%28x%29+=+x+%2F+%28x+%2B+1+%29

Find (f ◦ g)(3) and (g ◦ f)(3).

first find
(f ◦ g)(x) =f%28g%28x%29%29
(f ◦ g)(x) =f%28x+%2F+%28x+%2B+1+%29%29
(f ◦ g)(x) =sqrt%28x+%2F+%28x+%2B+1+%29%2B2%29
(f ◦ g)(x) =sqrt%28x+%2F+%28x+%2B+1+%29%2B2%28x+%2B+1+%29%2F%28x+%2B+1+%29%29
(f ◦ g)(x) =sqrt%28%28x+%2B2%28x+%2B+1+%29%29%2F%28x+%2B+1+%29%29
(f ◦ g)(x) =sqrt%28%28x+%2B2x+%2B+2+%29%29%2F%28x+%2B+1+%29%29
(f ◦ g)(x) =sqrt%28%283x+%2B+2+%29%29%2F%28x+%2B+1+%29%29
=>
(f ◦ g)(3) =sqrt%28%283%2A3+%2B+2+%29%2F%283+%2B+1+%29%29
(f ◦ g)(3) =sqrt%2811%2F4%29
(f ◦ g)(3) =sqrt%2811%29%2F2
(f ◦ g)(3) =1.658


(g ◦ f)(x) =g%28f%28x%29%29
(g ◦ f)(x) =g%28sqrt%28x%2B2%29%29
(g ◦ f)(x) =sqrt%28x%2B2%29+%2F+%28sqrt%28x%2B2%29+%2B+1+%29

=>
(g ◦ f)(3) =sqrt%283%2B2%29+%2F+%28sqrt%283%2B2%29+%2B+1+%29
(g ◦ f)(3) =sqrt%285%29+%2F+%28sqrt%285%29+%2B+1+%29
(g ◦ f)(3) =0.69