SOLUTION: Did I answer these correctly? 1.f(x) = 2x + 3 g(x)= 2x^2 + 2x Find f(g(x) ) 2(2x^2+2x)+3 =4x(x+1)+3 = 4x^2+4x+3 2. f(x) = 5x + 3 g(x) = 2x^2-2x + 2 Find (fg(x)

Question 1002814: Did I answer these correctly?
1.f(x) = 2x + 3
g(x)= 2x^2 + 2x
Find f(g(x) )
2(2x^2+2x)+3
=4x(x+1)+3
= 4x^2+4x+3
2. f(x) = 5x + 3
g(x) = 2x^2-2x + 2
Find (fg(x) )
(5x+3)(2x^2-2x+2)
2(5x+3)(x^2-x+1)
10x^3-4x^2+4x+6
3.f(x)=3x
g(x)= -2x^2 -2x
Find (f - g)(x)
3x-(-2x^2-2x)
=3x+2x^2+2x
=2x^2+5x
4.f(x)=3x + 1
g(x)=x^2-5x -2
Find g(f(x) )
(3x+1)^2-5(3x+1)-2
=6x+1+9x^2-15x-5-2
=9x^2-9x-6
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

1.f(x) = 2x + 3
g(x)= 2x^2 + 2x
Find f(g(x) )
=2(2x^2+2x)+3
=4x(x+1)+3
= 4x^2+4x+3 =>

2. f(x) = 5x + 3
g(x) = 2x^2-2x + 2
Find (fg)(x)
(5x+3)(2x^2-2x+2)
2(5x+3)(x^2-x+1)
10x^3-4x^2+4x+6 =>
3.f(x)=3x
g(x)= -2x^2 -2x
Find (f - g)(x)
3x-(-2x^2-2x)
=3x+2x^2+2x
=2x^2+5x =>
4.f(x)=3x + 1
g(x)=x^2-5x -2
Find g(f(x) )
(3x+1)^2-5(3x+1)-2
=6x+1+9x^2-15x-5-2
=9x^2-9x-6=>
great job!

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Did I answer these correctly?
1.f(x) = 2x + 3
g(x)= 2x^2 + 2x
Find f(g(x) = f(2x^2+2x) = 2(2x^2+2x)+3 = 4x^2 + 4x + 3
------------------------------------
2. f(x) = 5x + 3
g(x) = 2x^2-2x + 2
Find (fg(x) = f(2x^2-2x+3) = 5(2x^2-2x+3) + 3 = 10x^2 - 10x + 18
------------------------------------
3.f(x)=3x
g(x)= -2x^2 -2x
Find (f - g)(x) = f(x)-g(x) = 3x -(-2x^2-2x) = 2x^2 + 4x
-------------------------------
4.f(x)=3x + 1
g(x)=x^2-5x -2
Find g(f(x) = g(3x+1) = (3x+1)^2 - 5(3x+1) - 2
= 9x^2 + 6x + 1 - 15x - 5-2
= 9x^2 -9x -6
-----
Cheers,
Stan H.
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