Question

Functions Question

Answer 1

f(x)=6-4cos(1/2x)
6-4cos(1/2x)=4
-4cos(1/2x)=4-6=-4cos(1/2x)=-2 cos(1/2x)=1/2 Cosine is Positive in the first and 4th quadrant. cos(1/2x)=60, 360-60=300
1/2x=60, 1/2x=300
x=120 or 600 and 600 is obviously outside the range of x values.

Answer 2

@ganeshie8 Can you please help, its my last question and i am sorry i know i ask too much

Answer 3

How can i get the range?

Answer 4

@CGGURUMANJUNATH

Answer 5

@amistre64

Answer 6

the range if f(x) 6 +- 4

Answer 7

f(x)=6-4cos(1/2 x)

f(x)=6-4cos(2) is an exact value

Answer 8

what happened to the 1/2x

Answer 9

sorry, flipp[ing back and forth tends to jumble things up in my mind

Answer 10

f(x) = 4

6-4cos(x/2) = 4

2 = 4cos(x/2)

1/2 = cos(x/2)

cos^-1(1/2) = x/2

2cos^-1(1/2) = x

Answer 11

f(x)=6-4cos(1/2x)
6-4cos(1/2x)=4
-4cos(1/2x)=4-6=-4cos(1/2x)=-2 cos(1/2x)=1/2 Cosine is Positive in the first and 4th quadrant. cos(1/2x)=60, 360-60=300
1/2x=60, 1/2x=300
x=120-->2pi/3
yes thats what i got

Answer 12

for the domain

Answer 13

should we plug that in the f(x)

Answer 14

is in the stated domian (0 to 2pi)

Answer 15

i am stuck on that part the value 2pi/3 is the value of x in the stated domain

Answer 16

so the value*

Answer 17

f(2pi/3) = 4 yes

Answer 18

0 < 2pi/3 < 2pi

Answer 19

we solved for f(x) = 4, and determined x = 2pi/3

Answer 20

yes :), now comes the range part

Answer 21

well, what does cosine fluctuate between?

Answer 22

Cosine fluctuates between -1 and 1

Answer 23

then what we really have is a function from f(x) = 6-4(1) to 6-4(-1)

Answer 24

so the range of f lies between 2 and 10

Answer 25

yep

Answer 26

and to sketch it, youll want to determine the period

Answer 27

its slower than the usual function so i dont think itll have a period thats faster than it

Answer 28

For the sketch part, 1 period=120 degrees

Answer 29

cos(u) has a period of 2pi

cos(x/2) .... when does x/2 = 2pi?

Answer 30

Double that

Answer 31

then the period is 4pi .... which is half as fast as 2pi