Composite Functions
f(x) = 2x+3
g(x) = x2
Solve for g(f(x))
(2x+3)2
f-1(x) = (x-2)/4
Solve for x:
4x - 12(2x) + 32 = 0
x = 2, x = 3
Solve for x:
x = log381
4
Give the vertex of
y=-x2-4x-1
(-2, 3)
f(x) = 3x2+5
g(x) = 2/x
Solve for g(f(x))
2/(3x2+5)
Solve for the inverse of f(x) = x3+1
f-1(x) = cuberoot(x-1)
Solve for x:
16x - 14(4x) - 32 = 0
x=2
Solve for x:
x = log0.532
-5
A graph has x-intercepts at -1 and 3. It crosses (2, 6). What is the equation of the parabola?
f(x) = -2(x-3)(x+1)
or f(x) = -2x2+4x+6
f(x) = x2 - x - 2
g(x) = (x-2)/x
What is the domain of g(f(x))?
(-inf, -1) u (-1, 2) u (2,inf)
Solve for the inverse of f(x) = mx + b
f-1(x) = (x-b)/m
2x has been vertically stretched by 3, horizontally flipped, and then shifted down by 4. What is the equation of the transformation?
f(x) = 3(0.5)x - 4
Solve for x:
x = logsqrt(2)64
12
A quadratic equation with real coefficients has a root at (2+i)/3. It crosses (2, -51). What is the equation?
-27x2 + 36x - 15 = 0
If f(x) = 5x + 1 and f(g(x)) = 10x + 16, what is g(x)?
g(x) = 2x + 3
True/False: f(x) = x3-2x2-4x+8 has an inverse function
False. Does not pass y = 0 horizontal line test
Solve for x:
22x-1 - 3*2x-1 + 1 = 0
x = 0, x = 1
Solve for x:
x = log0.2532
-5/2
A parabola opens up the in second quadrant. It's vertex touches the x-axis. Describe the nature of a, b, c, and the discriminant in f(x) = ax2 + bx + c
a > 0, b > 0, c > 0, discriminant = 0
f(x) = 2x + 9/x
g(x) = x2 - 1
h(x) = sqrt(x)
What is h(g(f(x)))
sqrt((2x + 9/x)2-1)
Find the inverse of f(x) = x3-3x2+3x-10
f-1(x)=(x+9)^(1/3) + 1
Solve for x:
32x-5 - 28(3)x-3 + 9 = 0
x=5, x=2
If a = log10x and log636a=6, what is x?
1000
A car dealership sells only 35 new cars per month when the markup over factory price is $3000. For each $200 decrease in markup, the dealership can expect to sell an additional 5 cars. What is the maximum total profit that the dealership can make?
$121,000