Function Substitution & Operations

Operations on Functions

Dr. Tom Giles

What you'll learn today:

• Review what is a function

• Learn to substitute functions

• Perform operations on functions

What is Function?

• A relationship where every domain (x value has exactly one unique range y value)

• Functions is simply SUBSTITUTION!!!

Multiple Choice

What is the definition of function?

• Has inputs and outputs

• Every input has only ONE output

• Inputs have different outputs every time

• x-values and y-values

Multiple Choice

How do you read f(x)?

• f x

• f of x

• f times x

• f parenthesis x

Multiple Choice

f(x) is the same thing as _____.

• y

• x

• input

• an equation

Multiple Choice

If f(x) = 2x+1, what would the function look like once you substitute in a 1 to find f(1)?

• f(x) = 21+1

• f(1) = 2 (1) + 1

• f(1) = 2x (1) + 1

Multiple Choice

What is f(6) for the function f(x) = 3x - 8?

• -8

• 10

• -144

• answer not here

Multiple Choice

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x). 

• x²+x+9
• x²-x+9
• x²-x
• x²-x+18

Multiple Choice

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

• x²-2x+6
• -x²+2x+4
• -x²-2x-6
• x²-2x-4

Multiple Choice

Find g(x) = -3x + 10, given g(-2) .

• 6

• 16

• 26

• 36

Multiple Choice

f(x)=x³-3x
g(x)=-4x+1
Find f(x)*g(x)

• -4x³-5x²-3
• -4x³+2x²-3x
• -4x⁴+x³+12x²-3x
• -4x^4-x³+12x²⁺3x

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

• 19
• 23
• -10
• None of these.

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

• 16
• 4
• -4
• None of these.

Multiple Choice

p(x) = 3x + 4
q(x) = 2x²
Find q(p(-2))

• 8
• -8
• 28
• None of these.

Multiple Choice

If a question asks you to find f(2), what does that mean?

• Let x = 2

• Let y = 2

Multiple Choice

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

• 182
• 40
• 61
• None of the Above

Multiple Choice

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

• 11x² - 1
• 5x⁴ + 6x² - 1
• 5x² + 6x - 1
• 5x² + 8x - 1

Multiple Choice

When f(x) = x² - 9

and g(x) = x + 3 ,

find f(x) / g(x).

• x - 3

• x + 3

• x - 12

• x - 6

Multiple Choice

f(x)=2x + 4

g(x)=3x² - 1

Find f(x) ⋅ g(x)

• 6x⁴ + 12x³ - 4x² - 8x

• -6x³ + 12x² + 2x - 4

• 6x³ + 12x² - 2x - 4

• 5x² - 18x + 20

Multiple Choice

If f(x) = x - 1 and g(x) = 5x - 2, then (f + g) (x) =

• 5x² + 1

• 5x³ - 3

• 6x + 1

• 6x - 3

Multiple Choice

When f(x) = 2x and g(x) = x² + 3 , find f(g(x)).

• x² + 2x + 3

• 4x² + 3

• 2x² + 3

• 2x² + 6

Multiple Choice

• 4x² - 8x - 8

• 4x² - 8x

• 4x² - 8x - 8

• 4x² − 8x

Multiple Choice

f(x)= x² - 1

g(x)= x - 1

Find (f(x)/g(x))

Then simplify using x = 10

• 9

• 11

• 90

• 110

Multiple Choice

If f(x) = 2x and g(x) = 2x - 7, find f(x)/g(x).

• (2x - 7)/(2x)

• -7

• (2x)/(2x - 7)

• 1x - 3.5

Multiple Choice

If g(x) = 6x + 4 and f(x) = 3, find f(x) * g(x)

• 18x + 4

• 9x + 7

• 6x + 7

• 18x + 12

Multiple Choice

• -4x - 3

• -4x + 1

• 6x + 1

• 6x - 3

Multiple Choice

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x). 

• 14x-10
• -8x+2
• 2x+2
• 2x-2

Multiple Choice

• 2x² - 8x - 8

• 2x² + 8x - 8

• 2x² - 8x

• 2x² + 8x

Multiple Choice

• 5x - 3

• 5x² + 2

• 5x² - 7x + 2

• 5x - 7

Multiple Choice

• 4x + 1

• -2x + 3

• $$3x^2\ +\ 5x\ -\ 2$$

• $$\frac{x\ +\ 2}{3x\ -\ 1},\ x\ \ne\frac{1}{3}$$