Question

If f(x) = |sinx|+|cosx|, x is a real number, then what is the range of f(x)?

Answer 1

(A)f(x) belongs to [0,2]because sine and cosine lies between -1 to 1 hence their addition in mod might give either 0 or 2 therefore their range lies within 0 and 2 including 0 and 2

Answer 2

Answer:

[1,√2]

Step-by-step explanation:

To see the answer with mathematical logic click on the picture that is attached.

And to see how u can do it with desi logic read the para

i was also finding the answer of this question and i found different answers on internet. But i think that this answer suits the best because if you will increase the value of sinx then the value of cosx will decrease and therefore there is no point that its max value could be 2 which was the answer of many so called internet mathematicians and since there is mod the value will be greater than 0. With logic you can find that its max value will be at that point when the value of cosx and sinx would be same and its on 45° when value of sinx and cosx are same that is 1/√2 so if u add 1/√2 twice u will get ur max value as √2. About the min value u can see that the max difference between the values of sinx and cosx is 1 as when u are at 0° sinx will be 0 but cosx will be 1. now if u start increasing ur x then sinx will increase and cosx will decrease and ur min value of |sinx|+|cosx| will increase. so the min value would be 1.