Devin's Reflection

How to Find the Inverse of a Function:

• Replace f(x) with y
• Reverse the roles of x and y
• Solve for y in terms of x
• Replace y with f-1(x)
• check: should equal to x

Example:

f(x) = √x + 4

(x)^2 = (√y + 4)^2

x^2 = y + 4

y = x^2 - 4

f-1(x) = (x^2 - 4)

f(f-1(x)) = f(x^2 - 4) = √(x^2 - 4) + 4 = x

f-1(f(x)) = f-1(√x + 4) = (√x + 4)^2 - 4 = x + 4 - 4 = x

Logarithm Properties:

• logb MN = logb M + logb N
• logb M/N = logb M - logb N
• logb M^K = K logb M
• logb b^k = k
• b^logb^k = k

Changing Bases: (Done when you can't solve a log)

• Rewrite it as an exponential
• Take the log of both sides
• Move the variable to the front
• then solve

Example:

log5 10 = x

5^x = 10

log 5^x = log 10

x log 5 = 1

x = 1/log 5