Question

Find the range for the function f(x) = 1 + 3 cos x

Answer 1

Answer:

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Answer 2

Answer:

The range of f(x) is [-2, 4]

Step-by-step explanation:

• Range: Range means the minimum and maximum limit between which the value is situated.
• In question we have to calculate the range of f(x). That means we have to calculate the minimum and maximum possible value of f(x).
• Cos x: To determine the range of f(x), we need to know the range of cos x.

       For x = 0°, cos x = 1

       For x = 90°, cos x = 0

       For x = 180°, cos x = -1

       So the maximum value of cos x is 1 and minimum value of cos x is -1.

• Range of f(x) :

     (1) When cos x = 1, f(x) = 1 + 3(1) = 1 + 3 = 4

     (2) When cos x = -1, f(x) = 1 + 3(-1) = 1 - 3 = -2

   ∴ The minimum value of f(x) is -2 and maximum value of f(x) is 4.

       The range of f(x) is [-2, 4]

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