Question

If f(x) = { x, 2-X, x < 0 Osxs1. Determine h(x) = f(f(x)). x>1

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

( f(x)=left{begin{array}{ll}-x & x<0 x & 0 leq x leq 1 2-x & x geq 1end{array}right. ) for ( x<0 ) [ begin{array}{rl} f(x) & =f(f(x)) & =f(-x) & =-(-x)=x tan 0 & leq x leq 1 h(x) & =f(f(x)) & =f(x)=x log x & x^{prime}(x)=f(f(x)) & =f(2-x) & =2-(2-x)=x end{array} ] Therefore, ( h(x)=x ) far all ( x )