How do you find the domain and range of #2 csc x#?

1 Answer
Jul 1, 2018

Answer:

Domain : # x in RR , x != pi*n ; n# is an integer.
Range: # (-oo,2] uu [2,oo)#

Explanation:

# f(x)= 2 csc x = 2* 1/sin x#

Domain: All real number of #x# except #sin x=0# i.e

values of #x= pi*n# for all integers #n#

Domain : # x in RR , x != pi*n ; n# is an integer

Range: Since #csc x# is reciprocal of #sin x# ,

# f(x) <= -1 or f(x) >=1# for #csc x#

# f(x)= 2 csc x#

# :. f(x) <= -2 or f(x) >=2#

Range # (-oo,2] uu [2,oo)#

graph{2 csc x [-10, 10, -5, 5]} [Ans]