Composition Functions
f(x) = 3x and g(x) = 2x. Find (f\circ g)(x).
Plug g(x) into f(x).
(f\circ g)(x) = 3(2x) = 6x.
Find the inverse of
y=2x.
y^(-1) = 1/2x
Suppose $600 is deposited into an account that pays 7% annual interest compounded
yearly. Write an equation that gives the account balance A after t years.
A = $600(1+0.07)^t
Solve \sqrt{-x+1}-6=0
x = -35
f(x) = 3x and g(x) = 2x. Find (g\circ f)(x).
Plug f(x) into g(x).
(g\circ f)(x) = 2(3x) = 6x.
Find the inverse of
y=2x+6.
y^(-1) = (x-6)/2
Find the value of the investment after the specified time period: a $300 investment that earns 5% annual interest compounded yearly for 10
years.
300(1+0.05)^10=$488.67
Solve \sqrt{-5x+4}-8=0
x = -12
g(x) = 2x, f(x) = 3x^2, h(x) = 4x+1. Find (f\circ g\circ h)(x) .
(f\circ g\circ h)(x) = 3(2(4x+1))^2 = 12(4x+1)^2.
Find the inverse of
y=2x^2.
y^(-1) = sqrt(1/2x)
Find the value of the investment after the specified time period: a $500 investment that earns 2% annual interest compounded monthly for 30
years.
500(1+0.02/12)^(12*30)=$910.60
Daily Double. Solve (x+6)^(1/2)-x=0.
x=3
g(x) = 2x, f(x) = 3x^2, h(x) = 4x+1. Find (g\circ h\circ f)(x).
(g\circ h\circ f)(x) = 2(4(3x^2)+1) = 24x^2+2.
Find the inverse of
y=sqrt(3x).
y^(-1) = (x^2)/3
Find the value of the investment after the specified time period: a $1 investment that earns 100% annual interest compounded continuously for 2
years.
e^(1*2)=$7.39
(2x+10)^(1/3)-4=0. Solve for x.
x = 27
Find
(f^(-1) \circ f)(x).
(f^(-1) \circ f)(x) = x
Find the inverse of
y=5/4+5/3x.
y^(-1)=(12x-15)/20
Emmanuel wants to have $20,000 saved to buy a better car in 2 years, so he plans to deposit money into an account that pays 8% annual interest. How much money must he deposit now to reach his savings goal in 2 years if the interest is compounded yearly?
$20000 = P(1+0.08)^2 = 1.1664P
P = 20000/1.1664 = $17146.78
Solve ( 3x-6)^\frac{1}{2}+4=0
No solution