Question

let f:R = R: f (x)=|x| prove that fof =f

Answer 1

Step-by-step explanation:

f(x) = |x| represents the modulus function or absolute value function. It gives us the distance between any point and the origin. Since distance can never be negative so we always consider its positive value only.

now f(x)= x whenever x$\geqslant 0$

or f(x)=-x whenever x<0

now from L.H.S

fof= f(f(x))= f(x) if f(x)$\geqslant 0$

or f(f(x))= -f(x) if f(x)<0

now f(x) will positive if x $\geqslant 0$

and f(x) will negative of x <0

now these and |x| (called mod of x ) is always positive

so we can say that fof= f(f(x))= f(x)

thanks ragini singh