What is the range of cos^2(x)+2 ?

The range of cos^2(x)+2 is 2<= f(x)<= 3

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range of cos^2(x)+2

range

cos^{2} (x) + 2

2 \leq f (x) \leq 3

Interval Notation

[2, 3]

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

cos^{2} (x) + 2 : - \infty < x < \infty

Extreme Points of

cos^{2} (x) + 2 :

Maximum

(πn, 3),

Minimum

(\frac{π}{2} + πn, 2)

Find the range for the interval

- \infty < x < \infty : 2 \leq f (x) \leq 3

Combine the ranges of all domain intervals to obtain the function range

2 \leq f (x) \leq 3

- \frac{17}{13}

2 x^{2} + 4 x - 1

f (x) = \frac{5}{( x + 2 ) ( x - 1 )}

y = 3^{x + 2} - 1

f (x) = 100 (1 - \frac{x}{40})^{2}