Question

Find the range of f(x)= 1 + 3cos 2x

Answer 1

Let Y = 1 + 3 cos 2x

Now We Know that Cos Function lies
between -1 to 1

So putting These Value We get

Maximum Value = 1 + 3*1 = 4
Minimum Value = 1 + 3*(-1)= -2

So the range of f(x) is [-2,4]...


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Answer 2

Answer:

[-2,4 ] is the range of f(x) = 1+ 3cos2x

Step-by-step explanation:

Explanation:

Given , f(x) = 1 + 3cos2x

The range of a function y = f(x) is the set of all values of x for which the function is defined.

Now , as we know that the value of cos2x lies between [-1,1]

Step 1:

Therefore , -1≤ cos2x≤1

But we have 3cos2x , so multiply by 3 we get ,

-3≤ cos2x ≤ 3

Now from the given f(x) = 1+ 3cos 2x ,

⇒ -3 + 1≤ 1 + 3cos2x ≤ 3 + 1

⇒ -2 ≤ 1 + 3cos2x ≤4

∴f(x) ∈ [-2,4]

Final answer :

Hence, the range of  f(x) = 1 + 3cos2x is [-2,4].

SPJ2