Inverse Functions
The inverse of y = x - 7 is?
y = x + 7
How does the +5 affect the graph?
y = x2 + 5
Moves the graph up 5.
Multiply to see what is (x+2)(x-7) equivalent to?
x2 - 5x - 14
f(x) = 3x and g(x) = x+10
What is f(g(x))?
f(g(x))= 3(x+10)
or
f(g(x))= 3x+30
The inverse of f(x) = (x+4)2 is?
f-1(x) = squareroot of x - 4
How does the +5 affect the graph?
y = (x + 5)2
Moves the graph left 5.
Is the square root of 36 equal to the square root of 9 times the square root of 4?
yes
f(x) = 3x and g(x) = x+10
What is f(g(2))?
36
If x=3 gives an output of 7 in f(x),
then x=7 will give an output of __?__ in f-1(x).
3
How does the 5 affect the graph?
y = 5x2
Makes the graph 5 times as steep.
Is x2 + 5x - 6 equivalent to (x - 6)(x + 1)?
Yes
What happens when you compose a function and it's inverse?
You always get x!
Are these inverses of each other?
y = 4x - 5 and y = x/4 + 5
No
What shape is an Absolute Value function?
V-shaped
Is y = 5(3)x equivalent to y = 3(5)x ?
No or Only if x = 1
Think of a function that is its own inverse.
y = x or y = 1/x