Inverse Functions
What is the first step to finding the inverse of a function?
Replace f(x) with y
(Equally accepted answer)
Swap y with x
p(x) = 3x + 4
q(x) = 2x^2
Find p(q(x))
6x^2 + 4
If there were 20 flies in my backyard in the year 2010, but 200 flies in my backyard in the year 2011, make an equation using the Pe^rt formula.
A(t) = 20e^2.302t
log(5) + log(6)
log(30)
What line on a graph is the inverse of a function flipped over?
y=x
g(x) = 3x + 4
h(x) = 3x - 1
Find g(h(x))
9x + 1
I have 1,000,000 Twix bars from Halloween (very generous neighbors) and after eating them for 15 days I only have 350,000 left. Make a Pe^rt function using this data.
A(t) = 1,000,000e^-0.0699t
What property of logarithms is this:
log₉(20) = log(20)/log(9)
Change of Base Property
Find the inverse of the following function:
f(x) = 1/4x - 7
f^-1(x) = 4x + 28
f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))
4
There are 40 bacteria cells on my petri dish, and at the end of 300 days of letting them grow, they have only reached a measly 72 bacteria cells! What a flop! Make a function that represents this lousy bacteria using Pe^rt.
A(t) = 40e^0.001959t
Condense:
7log(v) + 3log(w)
logv⁷w³
Find the inverse of the following function:
f(x) = (x-2)/6
f^-1(x) = 6x + 2
f(x) = x^2 + x
g(x) = 3x + 1
Find f(g(4))
182
A single weed got into my garden and is rapidly growing more weeds with an exponential rate of 2.182. I checked back after a couple days and there was 6,700 weeds total! Use the Pe^rt formula to determine how many days have passed.
Around 4 days
Rewrite in logarithmic form:
3⁴ = 81
log₃(81) = 4
Find the inverse of the following function:
f(x)= x^4 - 2
f^-1(x) = ∜(x+2)
f(x) = x^2 - 4
h(x) = 3x + 3
Find f(h(x))
9x^2 + 18x + 5
A fairy gave me 50 bucks and told me that for each step I take, it will continuously compound with a rate of 0.0009. I just took one long jog today and I have 3 million bucks now! How many steps did I take? Use the Pe^rt formula to figure it out!
12,224 steps
Solve:
log₁₆(4) = x
1/2