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

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Answer 1 · 2018-07-01T12:15:49

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

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

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]

How do you find the domain and range of 2 csc x2 csc x?