If 0u

If 0u</2 and x=sec(u), then sqrt(x^21)=f(u), where...

Solution

x=sec(u)
so let us put x=sec(u) in sqrt(x^21)=f(u)
sqrt((sec^2(u)1)=f(u)

now, remember that sec² (u) – 1 = tan² (u)
so, our equation now becomes:
sqrt(tan^2(u))=f(u)
now we are given domain of u as 0u</2
so when u=0, f(0)=sqrt(tan²(0))=0
when u=/2 , f(/2)=sqrt(tan²(/2) )=infinity

So, range of the function is [0,infinity)