If f(x) = sin[π^2]x+sin[-π^2]x, where [x]denotes greatest Integer less than or equal to x, then

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Solution

Answer : f(x) = sin(9x) - sin(10x)

As we know that π = 3.14.

Then, (π)(π) ~ 9.(something) i.e. 9 < (π)^2 < 10

Now…

**greatest integer of (π)^2 = greatest integer of 9.(something) = 9

greatest integer of -(*π)^2 = greatest integer of -9.(something) = -10***

Substituting these values in f(x), we get…

f(x) = sin(9x) + sin(-10x),

f(x) = sin(9x) - sin(10x) [As: sin(-x) = -sin(x)]

You did not give specific value of x for which you want to know f(x) value i am going to give two example

Now,

f(π/2) = sin(9π/2) - sin (10π/2) = sin(9π/2) + sin(5π)

= sin(4π + π/2) - sin(4π + π)

= sin(π/2) - sin(π)

= 1 - 0 = 1

Similarly you can find any value of f(x) by simply substitute and find other values of f(x) when x is given.

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