how do i perform operations with function? 4.2 perform function operations and compositions example...
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• How do I perform operations with function?
4.2 Perform Function Operations and Compositions
Example 1 Add and subtract functionsAdd and subtract functions
following. theFind .5 and 3Let 22 xxgxxf xgxf a. xgxf b.
gfgf and ofdomain thec.Solution
xgxf a. 23x 25x 253 x ______________ 22x
xgxf b. 23x 25x 253 x ______________ 28x
4.2 Perform Function Operations and Compositions
Example 1 Add and subtract functionsAdd and subtract functions
following. theFind .5 and 3Let 22 xxgxxf xgxf a. xgxf b.
gfgf and ofdomain thec.Solutionc. The functions f and g each have the same domain:
_____________. So the domains of f + g and f – g also consist of ________________.
real numbersall real numbers
4.2 Perform Function Operations and Compositions
Checkpoint. Checkpoint. Perform the indicated operation. State the domain.Perform the indicated operation. State the domain.
xgxf 1.
.2 and 4Let 33 xxgxxf
34x 32x 32x
xgxf 2.34x 36x 32x
:Domain all real numbers
:Domain all real numbers
___________
4.2 Perform Function Operations and Compositions
Example 2 Multiply and divide functionsMultiply and divide functions
following. theFind . and 7Let 6xxgxxf
xgxf a. xgxf
b.
Solution
xgxf a. x7 6x 617 x 77x
________________________________________
b. xg
xf
7x6x
7 5x
g and ofdomain thec.f
gf
4.2 Perform Function Operations and Compositions
Example 2 Multiply and divide functionsMultiply and divide functions
following. theFind . and 7Let 6xxgxxf
xgxf a. xgxf
b.
Solutiong
and ofdomain thec.f
gf
c. The domain of f consists of ________________, and the domain of g consists of ________________. So, the
domain of f . g consists of ________________.
all real numbersall real numbers
all real numbers
Because g(0) = _____, the domain of is restricted to ______________________.
fg
0
all nonzero real numbers
4.2 Perform Function Operations and Compositions
Checkpoint. Checkpoint. Perform the indicated operation. State the domain.Perform the indicated operation. State the domain.
xgxf 3.
.2 and 4Let 33 xxgxxf
34x 8 32x
xgxf
4.
4 3x 232x
:Domain all real numbers
:Domain all nonzero real numbers
6x
___________________________________
4.2 Perform Function Operations and Compositions
Example 3 Find composition of functionsFind composition of functions
following. theFind .53 and 6Let 1 xxgxxf xgf a.
Solution xgf a. 53 xf 1 6 53 x
xfg b. xff c.n.compositioeach ofdomain thed.
53
6
x
_______________________________________________________
xfg b. 16 xg
5 3 16 x 518 1 x 518
x
_________________ xff c. 16 xf 1 6 16 x x166 x
4.2 Perform Function Operations and Compositions
Example 3 Find composition of functionsFind composition of functions
following. theFind .53 and 6Let 1 xxgxxf xgf a.
Solution
xfg b. xff c.n.compositioeach ofdomain thed.
d. The domain of f(g(x)) consists of ________________,
except x = ______ because is not in the
___________. (Not that f(0) = ____, which is __________.)
The domains of g(f(x)) and f(f(x)) consist of
_______________ except x = ____, again because
___________________________.
0_______
g
all real numbers
3
5
3
5 domain of f
6/0 undefined
all real numbers
0 0 is not in the domain of f
4.2 Perform Function Operations and Compositions
Checkpoint. Complete the following exercises.Checkpoint. Complete the following exercises. , a Find .3 and 45Let 5. 1 xgfxxgxxf
each ofdomain thed and , c , b xffxfgn.compositio
4 5 13 x a 415 1 x 415
x
1 3 45 x b
3
45 x
4 5 45 x c 42025 x 2425 x
Domain: all real numbers 0x
Domain: all real numbers5
4x
Domain: all real numbers
4.2 Perform Function Operations and Compositions
Example 4 Solve a multi-step problemSolve a multi-step problemYou purchase a computer with a price of $700. The computer store applies a store flyer coupon of $100 and a 12% promotional discount. Use composition to find the final price of the purchase when the coupon is applied before the discount. Use composition to find the final price of the purchase when the discount is applied before the coupon.
Step 1Write functions for the discounts. Let x be the original price, f(x) be the price after the $100 coupon, and g(x) be the price after the 12% promotional discount.
Function for the $100 coupon: ________xf 100xFunction for the 12% discount:
________xg xx 12.0 _____ x88.0
4.2 Perform Function Operations and Compositions
Example 4 Solve a multi-step problemSolve a multi-step problemYou purchase a computer with a price of $700. The computer store applies a store flyer coupon of $100 and a 12% promotional discount. Use composition to find the final price of the purchase when the coupon is applied before the discount. Use composition to find the final price of the purchase when the discount is applied before the coupon.
Step 2Compose the functions.
$100 coupon is applied first:
__________xfg 100xg ____________ 10088.0 x12% discount is applied first:
__________xgf xf 88.0 ____________ 10088.0 x
4.2 Perform Function Operations and Compositions
Example 4 Solve a multi-step problemSolve a multi-step problemYou purchase a computer with a price of $700. The computer store applies a store flyer coupon of $100 and a 12% promotional discount. Use composition to find the final price of the purchase when the coupon is applied before the discount. Use composition to find the final price of the purchase when the discount is applied before the coupon.
Step 3Evaluate the functions g(f(x)) and f(g(x)) when x = 700.
______________700 fg 10070088.0 ________ 60088.0 ____ 528$
______________700 gf 10070088.0 ________ 100616 ____ 516$
The final price is _____ when the $100 coupon is applied before the 12% discount. The final price is _____ when the 12% discount is applied before the $100 coupon.
528$516$
4.2 Perform Function Operations and Compositions
Checkpoint. Complete the following exercises.Checkpoint. Complete the following exercises.6. Rework Example 4 for an original price of $800, a $110
coupon, and a 15% discount.
110xxf xxxg 15.0 x85.0
xfg$110 coupon is applied first:
110x 85.0 xgf15% discount is applied first:
110x85.0 800fg
69085.050.586$
110800 85.0
800gf
110680 570$
110 80085.0
4.2 Perform Function Operations and Compositions
Pg. 123, 4.2 #1-31