SOLUTION: use f(x)=-2x+4 and g(x)=x^2-3x to determine or simplify the following (a)f(3) (b)g(-2) (c)g(f(3)) (d)f(g(x))

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 1204639: use f(x)=-2x+4 and g(x)=x^2-3x to determine or simplify the following
(a)f(3)
(b)g(-2)
(c)g(f(3))
(d)f(g(x))
Found 2 solutions by mananth, math_tutor2020:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
use f(x)=-2x+4 and g(x)=x^2-3x to determine or simplify the following
(a)f(3)
f(x)=-2x+4
f(3)=−2(3)+4=−6+4=−2

(b) g(-2)
g(x)=x^2-3x
g(−2)=(−2)^2−3(−2)=4+6=10

(c)g(f(3))
f(3)=−2.
g(-2) =(-2)^2 -(3)(-2)=10

Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

Part (a)

f(x) = -2x+4
f(3) = -2(3)+4
f(3) = -6+4
f(3) = -2

================================================================================
Part (b)

g(x) = x^2-3x
g(-2) = (-2)^2-3(-2)
g(-2) = 4+6
g(-2) = 10

================================================================================
Part (c)

g(f(3)) = g(-2) because f(3) = -2
We replace f(3) with -2

Then refer to part (b) to find that g(-2) = 10 which must mean g(f(3)) = 10

Here's another approach
g(x) = x^2-3x
g(x) = (x)^2-3(x)
g(f(x)) = ( f(x) )^2-3( f(x) )
g(f(x)) = (-2x+4)^2-3(-2x+4)
g(f(x)) = (4x^2-16x+16)+(6x-12)
g(f(x)) = 4x^2+(-16x+6x)+(16-12)
g(f(x)) = 4x^2 - 10x + 4

Then,
g(f(x)) = 4x^2 - 10x + 4
g(f(3)) = 4(3)^2 - 10(3) + 4
g(f(3)) = 4(9) - 10(3) + 4
g(f(3)) = 36 - 30 + 4
g(f(3)) = 6 + 4
g(f(3)) = 10
Your steps do not need to be as verbose as shown above.

================================================================================
Part (d)

f(x) = -2x + 4
f(x) = -2( x ) + 4
f(g(x)) = -2( g(x) ) + 4
f(g(x)) = -2( x^2-3x ) + 4
f(g(x)) = -2x^2 + 6x + 4

================================================================================

Summary of the four answers
f(3) = -2
g(-2) = 10
g(f(3)) = 10
f(g(x)) = -2x^2 + 6x + 4
Each answer can be verified with GeoGebra.