Q. 18 D5.0( 3 Votes )

Find the range of

Answer :

Given: f (x) = 1 + 3 cos2x


To find: the range of function


Explanation: So, the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range


Given,


f (x) = 1 + 3 cos2x


We know the value of cos 2x lies between -1, 1, so


-1≤ cos 2x≤ 1


Multiplying by 3, we get


-3≤ 3cos 2x≤ 3


Adding with 1, we get


-2≤ 1 + 3cos 2x≤ 4


Or, -2≤ f(x)≤ 4


Hence f(x) [-2, 4]


Hence the range of f = [-2, 4]


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