range of sin²x + sin x + 2
In this question, since sine ranges from -1 to 1, I thought that the minimum value would be when sin x gives us 0 (or -1 would work too), then we would get a result of 2. And for maximum, it would be when sin x is 1, so we get 4. So the range should have been [2,4] but this doesn't match any options.
I tried finding online solutions but there are none to this exact problem, and for similar problems, they add and subtract a value so as to form an equation in the form a² + b² + 2ab to take a whole square, I don't understand why would the do that when we know the range of sine already.
9 Replies
@Apu
Note for OP
+solved @user to close the thread when your doubt is solved. Mention the user who helped you solve the doubt. This will be added to their stats.complete the square on the sin
for example
we have f(x) range as (a,b) and g(x) range as (c,d)
for f(x)+g(x) we cant say the range is (a+c,b+d) or (a,b) U (c,d) as for different x's it might have diff f(x)'s g(x)'s
like its not nessasary for the minima/maxima of f(x) to be at the same as for g(x)
Hence we need to manupilate the question to form in such a way that we have * one * unique function to apply the range in . That happens to be sin x here
So we try to form it in a square , i can share a question i did which was similar to this so you get an idea
see the D1
here i had multiple |x| so i tried to make * one * |x| by completing the square
conclusion: you can't "add" ranges of diff functions together.
as it's not necessary they all will have the same maxima and minima and even critical points
Thank you so much for replying, so it means that we can still compute a composite function which is a sum of two other functions by taking some value of x, getting the results of those functions and adding both of them, but we can't know for sure that which combination will give us the smallest result so we reduce it to one function and then solve.
yeah i think you got the crux
Thank you so much!
+solved @Weirdo
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