What is the domain and range of #f(x) = 3+2sinx#?

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Answer 1 · 2017-01-31T13:14:18

#"The Domain = "RR," and, Range = "[1,5]#.

We will restrict our discussion in #RR#.

In #sin x#, we can take any real no. as #x,# which means that, the

Domain of #f# is #RR.#

Next, we know that, #AA x in RR, -1 le sinx le 1#.

Multiplying by #2>0, -2 le 2sinx le 2,# &, adding #3#,

# -2+3 le 3+2sinx le 2+3 rArr 1 le f(x) le 5.#

#:." The Range of "f" is "[1,5]#.

Enjoy Maths.!