MATH10-4 homework on operations on functions.pdf

10/24/13 MATH10-4 homework on operations on functions

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1. 8/8 points | Previous Answers AufCATINT7 2.6.001.

Use the given functions f and g to find State the domain of each.

Domain:

Domain:

MATH10-4 homework on operations on functions (Homework)

Irous Chester Lipardo

MATH10-4, section A1, Fall 2013Instructor: Lilibeth Sabino

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f + g, f − g, fg, and .f

g

f(x) = x2 − 8x − 20, g(x) = x + 2

f + g =

(-∞,0) ∪ (0, ∞)

(-∞, -2) ∪ (-2, ∞)

(-20, 8)

(-∞, ∞)

(-∞, 10) ∪ (10, ∞)

(8, 20)

f − g =



Domain:

Domain:

(-∞, -2) ∪ (-2, ∞)

(-∞, ∞)

(-∞,0) ∪ (0, ∞)

(-20, 8)

(-∞, 10) ∪ (10, ∞)

(8, 20)

fg =

(-∞, ∞)

(-20, 8)

(8, 20)

(-∞, -2) ∪ (-2, ∞)

(-∞, 10) ∪ (10, ∞)

(-∞,0) ∪ (0, ∞)

=

f

g





Domain:

Domain:

(-∞, -2) ∪ (-2, ∞)

(-∞, ∞)

(-20, 8)

(8, 20)

(-∞,0) ∪ (0, ∞)

(-∞, 10) ∪ (10, ∞)


g

f(x) = 4x + 12, g(x) = x + 3

f + g =

(−∞, ∞)

(−∞, −3) ∪ (−3, ∞)

(−∞, 3) ∪ (3, ∞)

{3}

(−∞, 0) ∪ (0, ∞)

(−∞, −12) ∪ (−12, ∞)

f − g =



Domain:

Domain:

(−∞, ∞)

(−∞, −3) ∪ (−3, ∞)

(−∞, 3) ∪ (3, ∞)

{3}

(−∞, 0) ∪ (0, ∞)

(−∞, −12) ∪ (−12, ∞)

fg =

(−∞, ∞)

(−∞, −3) ∪ (−3, ∞)

(−∞, 3) ∪ (3, ∞)

{3}

(−∞, 0) ∪ (0, ∞)

(−∞, −12) ∪ (−12, ∞)

=

f

g





Domain:

Domain:

(−∞, ∞)

(−∞, −3) ∪ (−3, ∞)

(−∞, 3) ∪ (3, ∞)

{3}

(−∞, 0) ∪ (0, ∞)

(−∞, −12) ∪ (−12, ∞)


g

f(x) = x3 − 9x2 + 2x, g(x) = x

f + g =

(−∞, ∞)

(−∞, −2) ∪ (−2, ∞)

(−∞, 2) ∪ (2, ∞)

{2}

(−∞, 0) ∪ (0, ∞)

(−∞, −9) ∪ (−9, ∞)

f − g =



Domain:

Domain:

(−∞, ∞)

(−∞, −2) ∪ (−2, ∞)

(−∞, 2) ∪ (2, ∞)

{2}

(−∞, 0) ∪ (0, ∞)

(−∞, −9) ∪ (−9, ∞)

fg =

(−∞, ∞)

(−∞, −2) ∪ (−2, ∞)

(−∞, 2) ∪ (2, ∞)

{2}

(−∞, 0) ∪ (0, ∞)

(−∞, −9) ∪ (−9, ∞)

=

f

g





Domain:

Domain:

(−∞, ∞)

(−∞, −2) ∪ (−2, ∞)

(−∞, 2) ∪ (2, ∞)

{2}

(−∞, 0) ∪ (0, ∞)

(−∞, −9) ∪ (−9, ∞)


g

f(x) = , g(x) = −xx − 10

f + g =

(-∞,0) ∪ (0, ∞)

(-∞,10) ∪ (10, ∞)

(-∞, ∞)

(10, ∞)

(-∞, 10]

[10, ∞)

f − g =



Domain:

Domain:

(10, ∞)

(-∞,0) ∪ (0, ∞)

(-∞, ∞)

(-∞, 10]

[10, ∞)

(-∞,10) ∪ (10, ∞)

fg =

(-∞,10) ∪ (10, ∞)

[10, ∞)

(-∞, ∞)

(-∞, 10]

(-∞,0) ∪ (0, ∞)

(10, ∞)

=

f

g





Domain:

Domain:

(-∞, 10]

(-∞,10) ∪ (10, ∞)

(10, ∞)

(-∞, ∞)

(-∞,0) ∪ (0, ∞)

[10, ∞)


g

f(x) = , g(x) = 4 + x16 − x2

f + g =

(−∞, ∞)

[−4, 4]

(−∞, −16) ∪ (−16, ∞)

(−4, 4)

(−∞, 0) ∪ (0, ∞)

(−∞, −4) ∪ (−4, ∞)

f − g =



Domain:

Domain:

(−∞, ∞)

[−4, 4]

(−∞, −16) ∪ (−16, ∞)

(−4, 4)

(−∞, 0) ∪ (0, ∞)

(−∞, −4) ∪ (−4, ∞)

fg =

(−∞, ∞)

[−4, 4]

(−∞, −16) ∪ (−16, ∞)

(−4, 4)

(−∞, 0) ∪ (0, ∞)

(−∞, −4) ∪ (−4, ∞)

=

f

g




Evaluate (f + g)(−6).

,

-20

(−∞, ∞)

(−4, 4]

(−∞, −16) ∪ (−16, ∞)

(−4, 4)

(−∞, 0) ∪ (0, ∞)

(−∞, −4) ∪ (−4, ∞)

f(x) = x2 − 6x + 9 g(x) = 4x − 5



7. 1/1 points | Previous Answers AufCATINT7 2.6.022.MI.

Evaluate the indicated function, where

-200

Master It

Evaluate the indicated function, where

Part 1 of 2

To find for the given functions, use the definition of operations on functions that states

that if f and g are functions with domains and then we define the product as

and the domain of the function is

Now substitute f and g in the definition stated above, and simplify.


Find for the given functions f and g.

f(x) = x2 − 3x + 2 and g(x) = 2x − 4.

(fg)(−3)

f(x) = x2 − 3x + 2 and g(x) = 2x − 4.

(fg)(−6)

(fg)(x)

Df Dg,

(f · g)(x) = f(x) · g(x), f · g Df ∩ Dg.

(fg)(x) = f(x) · g(x)

= (x2 − 3x + 2) · (2x − 4)

= 2x(x2 − 3x + 2) − (No Response) (x2 − 3x + 2)

= 2x3 − 6x2 + 4x − (No Response) x2 + 12x − 8

= (No Response)

(g f)(x) and (f g)(x)

f(x) = 4x − 8, g(x) = 3x + 1

(g f)(x) =

(f g)(x) =




Find (g f)(x) and (f g)(x).

10.2/2 points | Previous Answers AufCATINT7 2.6.041.


f(x) = x2 + 6x − 3, g(x) = x + 7

(g f)(x) =

(f g)(x) =


f(x) = x3 + 6x, g(x) = −4x

(g f)(x) =

(f g)(x) =






f(x) = , g(x) = 5x − 77

x + 3

(g f)(x) =

(f g)(x) =



12.0/1 points | Previous Answers AufCATINT7 2.6.050.MI.

Evaluate the composite function, where

176

Master It


Part 1 of 3

Composition of functions is another method in which functions can be combined. In this method,

the output of one function is used as the input for a second function.

Recall the definition of composition of two functions− let f and g be two functions such that

is in the domain of f for all x in the domain of g. Then the composition of the two functions,

denoted by is the function whose value at x is given by

It is given that and Now find (f g)(x).

By the definition of composition of the two functions,

Substitute for x in



60

f(x) = 2x + 3, g(x) = x2 − 5x, and h(x) = 4 − 3x2.

(f g)(4)

f(x) = 2x + 3, g(x) = x2 − 5x, and h(x) = 4 − 3x2.

(f g)(6)

g(x)

f g, (f g)(x) = f[g(x)].

f(x) = 2x + 3 g(x) = x2 − 5x.

(f g)(x) = f[g(x)].

g(x) f(x) = 2x + 3.

f[g(x)] = 2(g(x)) + (No Response)

f(x) = 3x + 6, g(x) = x2 − 5x, and h(x) = 4 − 3x2.

(f f)(4)





15.–/2 points AufCATINT7 2.6.044.


f(x) = 2x + 3, g(x) = x2 − 5x, and h(x) = 2 − 5x2.

(h g)(k − 1)


f(x) = , g(x) = x + 71

x

(g f)(x) = (No Response)

(f g)(x) = (No Response)

MATH10-4 homework on operations on functions.pdf

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