How do you find the domain and range of $y= .5cos(x/2-2sqrt3)+1$ ?

Question

1478 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-10T06:30:15

The domain is $x in RR$
The range is $y in [0.5, 1.5]$

By definition, cosine is defined over $RR$

so, the domain is $=RR$

The range of cosine is

$-1<= cos(x/2-2sqrt3)<=1$

Multiply by $0.5$

$-1*0.5<= 0.5*cos(x/2-2sqrt3)<=1*0.5$

$-0.5<= 0.5*cos(x/2-2sqrt3)<=0.5$

Add $1$

$-0.5+1<= 0.5*cos(x/2-2sqrt3)+1<=0.5+1$

$+0.5<= 0.5*cos(x/2-2sqrt3)+1<=1.5$

$+0.5<= y <=1.5$

How do you find the domain and range of y= .5cos(x/2-2sqrt3)+1y= .5cos(x/2-2sqrt3)+1?