Review

Inverse Function

100

Find the inverse function:

F(x) = (2/3)x+3

F'(x) = (2/3)x-2

200

Find the inverse function:

F(x) = e^(2x-3)

F'(x) = 1 + ln(x)/3

300

Find the inverse of the following:

h(x) 

h'(x) = ln(x/4)/ln(1/2)

400

Find the inverse Function:

F(x) = log(e^100x-10)

F'(x) = (xln(10) + 10)/100

Exponentials

100

The car was bought for $10,000 in 2000. The price in 2010 decreased to $5,000.

Find the value of a car in 2023 using an exponential model.

$2030.63

200

Solve this exponential using Desmos:

F(x) = 2*(e)^x

F(x) = 4

On desmos type the following:

y = 2e^x

y = 4

They should cross at x = 0.693.

300

Solve the Exponential Using Definition of Log:

y = 23(1/3)^x-5

y = 25

x = 5+ log_1/3(25/23)

or 

x = 5 + ln(25/23)/ln(1/3)

x = 4.924

400

Solve using logs on both sides:

5^x+y= e^7x

^{Solve for y}

y= 7x/ln(5) -x

Composition of Functions

100

Determine composition of functions for w(x).

g(x) = x-1

f(x) = 2^x

f(g(x))

200

Using h(x) and w(x) solve c(x)

c(x) = h(x) * w(x)

2

300

Simplify the following j(x) = z(x) - y(x)

j(x) = x²+3x+2

400

Find f(w(y(x)))

-3(2^-3w)+1

Function Questions

100

Find the quadratic equation for g(x)

g(x) = -2(x+1)²+3

200

Find the intervals where k(x) is decreasing when the domain is restricted to [-2,4].

(-2,-1.5)U(-0.5,0.5)U(1.5,2.5)U(3.5,4)

300

Solve z(x) = 0

Not a solution

400

What is the domain and range of k(x)

Domain: (-infinity, infinity)

Range: [-3,5]