SOLUTION: How do I solve these kind of questions: 1) f(x)=2x+3, g(x)=x^2-1, find (fog)(3) 2) f(x)=3x-2, g(x)=x+2 / 3, find (fog)(x) 3) f(x)= root x, g(x)=-x^2-2, find (fog)(x) 4) f(x)=x^

Algebra ->  Functions -> SOLUTION: How do I solve these kind of questions: 1) f(x)=2x+3, g(x)=x^2-1, find (fog)(3) 2) f(x)=3x-2, g(x)=x+2 / 3, find (fog)(x) 3) f(x)= root x, g(x)=-x^2-2, find (fog)(x) 4) f(x)=x^      Log On


   

Question 787140: How do I solve these kind of questions:
1) f(x)=2x+3, g(x)=x^2-1, find (fog)(3)
2) f(x)=3x-2, g(x)=x+2 / 3, find (fog)(x)
3) f(x)= root x, g(x)=-x^2-2, find (fog)(x)
4) f(x)=x^2-1, g(x)=x^2+1, find (fog)(x) - (gof)(x)
Thank you.
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve these kind of questions:
1) f(x)=2x+3, g(x)=x²-1, find (f∘g)(3)
(f∘g)(3) = f(g(3))

Find g(3) by substituting x=3 in g(x)

g(x)=x²-1
g(3)=3²-1
g(3)=9-1
g(3)=8

f∘g(3) = f(g(3)) = f(8)

find f(8) by substituting x=8 in f(x):

f(x)=2x+3
f(8)=2(8)+3
f(8)=16+3
f(8)=19

So f∘g(3) = 19

-------------------------

2) f(x)=3x-2, g(x)=%28x%2B2%29%2F3, find (f∘g)(x)
(f∘g)(x) = f(g(x)) = f%28%28x%2B2%29%2F3%29

Find f%28%28x%2B2%29%2F3%29 by replacing x by
%28x%2B2%29%2F3 in f(x)

f(x)=3x-2
f%28%28x%2B2%29%2F3%29=3%28%28x%2B2%29%2F3%29-2
f%28%28x%2B2%29%2F3%29=(x+2)-2
f%28%28x%2B2%29%2F3%29=x+2-2
f%28%28x%2B2%29%2F3%29=x
So
(f∘g)(x) = x
---------------------------

3) 
f(x) = √x
, g(x)=-x²-2, find (f∘g)(x)
(f∘g)(x) = f(g(x)) = f(-x²-1)

Find f(-x²-1) by replacing x by
-x²-1 in f(x)

f(x) = √x
f(-x²-1) = √-x²-1

So 
(f∘g)(x) = √-x²-1 

--------------------------

4) f(x)=x²-1, g(x)=x²+1,
find (f∘g)(x) - (g∘f)(x)
(f∘g)(x) - (g∘f)(x) =

f(g(x)) - g(f(x)) =

f(x²+1) - g(x²-1) =

[(x²+1)²-1] - [(x²-1)²+1] =

[x²+2x+1-1] - [x²-2x+1+1] =

[x²+2x] - [x²-2x+2] =

x²+2x-x²+2x-2 =

4x-2

Edwin