Function Operations
f(x) = 5x2 - 4
g(x) = 3x2 + 6
What is f+g(x)?
f+g(x) = 8x2 + 2
f(x) = 2x2 + 4
g(x) = x - 2
What is f(g(2))?
f(g(2)) = 4
Has to be one-to-one: One input maps to one and only one output! can never have multiple outputs for a single input!
Create the table for the inverse of the function below.
x | f(x)
3 | 4
4 | 6
5 | 8
x | f -1 (x)
4 | 3
6 | 4
8 | 5
Find the inverse equation for the function below:
f(x) = 6x - 18
f -1 (x) = 1/6 x + 3
f(x) = 4x2 + x - 1
g(x) = x2 - 2x + 3
What is f(x) - g(x)?
f(x) - g(x) = 3x2 + 3x - 4
f(x) = 4x2 - 8x + 7
g(x) = 3x - 4
g(f(-1)) = ?
g(f(-1)) = 53
If the Domain of f(x) is x > 2, then what is the range of f -1 (x)?
y > 2
Will the inverse of the function represented in the table below truly be a function? Why or why not?
x | f(x)
7 | 2
0 | 0
4 | 2
The inverse is not a function, 1 input x |f -1 (x) can not have 2 different outputs
2 | 7
0 | 0
2 | 4
Find the inverse equation for the function below:
f(x) = 5x + 12
f -1 (x) = 1/5 x - 2.4
f(x) = 3x2 + 2x + 3
g(x) = -2x2 - x + 4
What is g-f(x)?
g-f(x) = -5x2 - 3x + 1
f(x) = x2 + 3x - 5
g(x) = 4x + 6
g ° f (3) = ?
g ° f (3) = 58
Sometimes we must restrict the domain of a function so that its inverse is a ____________ .
one-to-one function
Using the table below, find f -1 (2)
x |f(x)
2 | 0
3 | 1
4 | 2
f -1 (2) = 4
Find the inverse equation for the function below:
f(x) = x2 + 4, x > 0
f -1 (x) = √(x-4) , y > 0
A gardening company earns a revenue, r(x) = 12x + 100 where x are the number of plants planted each month. If the company's monthly cost is modeled by c(x) = 3x - 50, what function can be used to model their profit p(x)?
p(x) = 9x + 50
BONUS POINT: If the company plants 650 flowers and 400 vegetables last month, what is their profit?
f(x) = 3x2 + 2x - 1
g(x) = 6x - 4
What is g(f(x))?
g(f(x)) = 18x2 + 12x - 10
On the function g(x), the point (5, 4) can be found. Which of the following points can be found on g -1 (x)?
A. (-5, 4) C. (-5, -4)
B. (-4, 5) D. (4, 5)
D. (4, 5)
BONUS POINT: How do we know this point will be on the inverse without having any other information about the graph?
Write any (x, y) point that can be found on the inverse of the function represented by the table below.
x |f (x)
3 | 6
4| 9
5 | 12
Possible answers: (6,3), (9,4), (12,5)
Find the inverse equation for the function below:
f(x) = √(2x - 4) , x > 2
f -1 (x) = 1/2 x2 + 2 , y > 2
Marco is wanting to install a pool into his backyard. The area of his backyard can be modeled by the equation y(x) = 4x2 - 5x + 6. The pool he wants to install has an area of p(x) = 2x2 + 2x - 4. What equation can model the area remaining in Marco's yard after installing the pool?
Remaining area: 2x2 - 7x + 10
f(x) = x2 - 4x + 3
g(x) = 5x - 2
f ° g(x) = ?
f ° g(x) = 25x2 - 40x + 15
Using what you know about inverses, fill in the missing piece below:
f (4) = 8
f -1 (8) = ?
4
Create a table to represent the inverse of a function that contains the points (3, 4), (9, 12), and (15, 20)
x |f -1 (x)
4 | 3
12 | 9
20 | 15
DOUBLE JEOPARDY!! DOUBLE POINTS!!
Find the equation of a function whose inverse is represented by f -1 (x) = 1/6 x2 - 3 , y > -3
f(x) = √(6x + 18) , x > -3