Find the range of:

f(x)=ιsinxι+ιcosxι, 0≤x≤π

where ιxι represents modulus of x.

Hi Menka,

Here you split the domain into two parts,

0≤x≤Π/2------------ Domain(1) and Π/2≤x≤Π----------Domain(2).

In D1, the function becomes f(x) = sinx+cosx = (√2)*(sin(x+Π/4),

In this domain sin(x+pi/4) lies in [1/√2,1]

Hence f(x) will lie in the range [1,√2].

Next in D2, the function becoemes f(x) = sinx - cosx = root(2)*sin(x-pi/4)

In this domain sin(x-pi/4) again lies in [1/√2,1]

Hence f(x) will lie in [1,√2].

Hence the range of this function is [1,√2].

Hope that helps.

All the best,

Regards,

Ashwin (IIT Madras).