1.7 combinations of functions

Domain

100

find the domain of g/f

g=2x-1

f=x-8

(-∞ ,-8 )(-8,∞ )

100

find the domain of f/g

f=-2x+9

g=x-4

(-∞ ,-4)(-4,∞ )

100

find the domain of f/g

f=7x+4

g=x+4

(-∞ ,4)(4,∞ )

100

find the domain of g/f

g=6x²-8x+9

f=x-9

(-∞ ,-9)(-9,∞ )

100

find the domain of f/g

f= 3x+2

g=7x-9

(-∞ ,-14)(-14,∞ )

adding and subtracting

100

find f-g

f= 3x+7

g= x²+6x+2

-x²-3x+5

100

find g-f

f=4x²-8x+6

g=-2x-9

-4x²+6x-15

100

find f+g 

f= 5x²-9x+3

g=3x²-4x+8

8x²-13x+11

100

find g+f

2x²+9x-4=f

-7x²+8x-9=g

-5x²+17x-13

100

find f=g

6x²+4x-7=f

6x-2=g

6x²+10x-9

multiplying and divding

100

find f(x) x g(x)

g= 2x-5

f=3x

6x²-15x

or x(6x-15)

100

(f/g)(-3)

f(x) = 3x²-13

g(x) = -2x+16

7/11

100

find f/g

f(x) = x²-2x-3

g(x) = x²-1

(x-3)/(x-1)

100

find f(x) x g(x)

f= 13x-21

g=8x+7

104x²-77x-147

100

find (f/g)(x) 

f(x) = 3x²+x+9

g(x) = x²+1

3+(x+6)/(x²+1)

(F of G)(x)

100

find g of f

f= 3x-3

g=2x²-8x+7

18x²-24x+49

100

find f of g

f= 2x+9

g=-2x²+7x-8

-4x²+14-5

100

find f[g(2)]

f=3x²-2x+3

g=4x-3

68

100

find g[f(4)]

f= -x²+7x-4

g=3x²-4x-3

4

100

find g[f(8)]

f=6x²-4x-9

g=7x²-12x+13

866,606

definitions

100

                           

Define domain

The set of all real numberrs, (-∞ , ∞ ), unless x appears in a denominator or in an even root, such as a square root.

100

What is the domain of f+g?

The domain of f+g is the set of all real numbers that are common to the domain of f and the domain of g.

100

What are "The Algebra of Functions"?

The sum f+g, the difference f-g, the product fg, and the quotient f/g, are functions whose domains of f and g (D_f∩D_g).

100

What is a composite function?

A composite function, or composition of the function f with g, is a function whose values are found from two given functions by applying one function to an independent variable and then applying the second function to the result and whose domain consists of those values of the independent variable for which the result independent variable for which the result yielded by the first function lies in the domain of the second.

For example, f[g(x)] is the composite function of f(x) and g(x). It is read as "f of g of x" (fog)(x)

100

What does it mean to decompose functions?

When you form a composite function, you "compose" two functions to form a new function. When you reverse this process, you can "decompose" a given function and express it as a composition of two functions.