Combining Functions
f(x)= 16x2 + 8x - y + z
g(x)= -z + y - 8x - 16x2
Find f(x) + g(x)
f(x) + g(x) = 0
f(x) = x
g(x) = x2
Find f(g(x))
f(g(x)) = x2
Find the inverse of the following relation.
y = -x
y = -x
Find the 4th term in the function (1 + p)4
Hint: Find the p3 term
4p3
How do you know a function is a factor of another function using synthetic or long division?
The remainder, R, is 0
f(x)= 9x4 + 18x3 - 9y + 1
g(x)= -8x3 + x -9
Find f(x) - g(x)
f(x) - g(x) = 9x4 + 26x3 - x - 9y + 10
f(x)= 3x + 7
g(x)= x3 + 1
Find f(g(3))
f(g(3)) = 91
Find the inverse of the following relation.
y = 12x - 3
y = 1/12x + 1/4
Fully expand the following function using Pascal's triangle:
(1 + x)6
x6 + 6x5 + 15x4 + 20x3 + 15x2 + 6x + 1
Use synthetic or long division to solve the following:
(x3 – 2x + 1) / (x – 1)
x2 + x – 1
f(x)= 2a3b2c - 4a2bc + 6a4b2c2
g(x)= 2a2bc
Find f(x) / g(x)
f(x) / g(x) = ab - 2 + 3a2bc
f(x) = x2 - x
g(x) = x + 3
Find f(g(x))
f(g(x)) = x2 + 5x + 6
Find the inverse of the following relation.
y = (x + 3)2
y = 3 + root 2 (x)
Find the coefficient of the x2 term in the function
(2x + 3)4
216x2
What is the remainder, R, of the following problem?
(4x3 – 10x2 – 11x + 16) / (x – 4)
68
f(x)= -4x + 7 + 2x3
g(x)= 9 + 7x
Find f(x)g(x)
f(x)g(x) = 14x4 + 18x3 - 28x2 +13x + 63
f(x) = x2 - 2x + 1
g(x) = x - 5
Find f(g(2))
f(g(2)) = 16
Find the inverse of the following relation.
y = root 2 (x-2)
y = x2 + 2
Find the coefficient of the a2b3 term in the expansion
(a + 2b)5
80a2b3
Use synthetic or long division to solve the following:
(12x3 - 11x2 + 9x + 18) / (4x + 3)
3x2 - 5x + 6
f(x)= 2x3y + 4xy - 3
g(x)= 4x2y2 - 5x
Find f(x)g(x)
f(x)g(x) =
8x5y3 - 10x4y + 16x3y3 - 20x2y - 12x2y2 + 15x
f(x) = 2x2 - 6x + 1
g(x) = x + 3
Find f(g(2x))
f(g(2x)) = 8x2 + 12x + 1
Are the two functions below inverses?
f(x) = -(x+1)3
g(x) = 3 + x3
No
Find the coefficient of the x4 term of the function
(95x2 + 32)3
866400x4
What is the remainder, R, of the following problem?
(2x3 - 4x + 7x2 + 7) / (x2 + 2x - 1)
-8x + 10