mathdad
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- Apr 24, 2015
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Given f(x) = -x^2 + 3 and g(x) = -3x + 3, solve A and B.
A. f(x) > g(x)
B. f(x) = g(x)
Solution for A
f(x) > g(x)
-x^2 + 3 > -3x + 3
-x^2 + 3 + 3x - 3 > 0
-x^2 + 3x > 0
x(-x + 3) > 0
x(3 - x) > 0
<-------0-----------3--------->
Select a number from each region.
Let x = -1
-(-1)^2 + 3(-1) > 0
-1 - 3 > 0
-4 > 0 is false.
Let x = 1
-(1)^2 + 3(1) > 0
-1 + 3 > 0
2 > 0 is true.
Let x = 4
-(4)^2 + 3(4) > 0
-16 + 12 > 0
-4 > 0 is false.
Solution: (0, 3).
Is this right?
Solution for B
f(x) = g(x)
-x^2 + 3 = -3x + 3
Solve for x.
-x^2 + 3x = 3 - 3
-x^2 + 3x = 0
Factor left side.
x(-x + 3) = 0
x = 0
-x + 3 = 0
-x = -3
x = -3/-1
x = 3
Correct?
A. f(x) > g(x)
B. f(x) = g(x)
Solution for A
f(x) > g(x)
-x^2 + 3 > -3x + 3
-x^2 + 3 + 3x - 3 > 0
-x^2 + 3x > 0
x(-x + 3) > 0
x(3 - x) > 0
<-------0-----------3--------->
Select a number from each region.
Let x = -1
-(-1)^2 + 3(-1) > 0
-1 - 3 > 0
-4 > 0 is false.
Let x = 1
-(1)^2 + 3(1) > 0
-1 + 3 > 0
2 > 0 is true.
Let x = 4
-(4)^2 + 3(4) > 0
-16 + 12 > 0
-4 > 0 is false.
Solution: (0, 3).
Is this right?
Solution for B
f(x) = g(x)
-x^2 + 3 = -3x + 3
Solve for x.
-x^2 + 3x = 3 - 3
-x^2 + 3x = 0
Factor left side.
x(-x + 3) = 0
x = 0
-x + 3 = 0
-x = -3
x = -3/-1
x = 3
Correct?