Question

f(x) = cos(x - 4) - 8
find the inverse function of the function f

Answer 1

y= cos(x-4) -8
cos(x-4) = y+8
x-4 =cos^{-1}(y+8)
x=4+ cos^{-1}(y+8)
so the inverse is 4+ cos^{-1}(y+8)

Answer 2

y=cos(x-4)-8 (you should define a domain for this function that will make the function 1 to 1)
y+8=cos(x-4)
cos^{-1}(y+8)=x-4
cos^{-1}(y+8)+4=x
f^{-1}(x)=cos^{-1}(x+8)+4

Answer 3

sin(cos-1 1/2 - sin-1 squareroot 3 over 2) --> how do you find the exact value of this??

Answer 4

cos^{-1}(1/2)=a
cosa=1/2
so a=pi/3
sin^{-1}(sqrt{3}/2)=b
sinb=sqrt{3}/2
so b=pi/3
sin(pi/3-pi/3)=sin(0)=0

Answer 5

dang thanks!!

Answer 6

cos(tan-1 5/12 - cos-1 4/5)
its multiple choice
A) 7/13
B)63/65
c)52/65
d)13/24

Answer 7

thats simple

Answer 8

B

Answer 9

let a be the first thing, b be the second

and expand

Answer 10

also you can just put it in you calculator
and then look at the fractions to see which one it is

Answer 11

thats the cheating way

Answer 12

sin[pi/4 + x] = squareroot2(cos x + sin x)

Answer 13

I'm suppose to establish the identity

Answer 14

you can express tan inverse in terms of cos inverse as tan^(-1) (a/b)= cos^(-1) (b/sqrt(a^2+b^2))
then use cos^(-1) a + cos^(-1) b formula to find the answer

Answer 15

thanks shankvee!!!!! for all your help!