The Total solution for NCERT class 6-12
Let R+ be the set of all non-negative real numbers.If f: R+ → R+ and g : R+ → R+ aredefined as f(x)=x2 and g(x)=+ √x, find fog and gof.Are they equal functions.
Given f: R+ → R+ and g: R+ → R+So, fog: R+ → R+ and gof: R+ → R+Domains of fog and gof are the same.
Now we have to findfog and gof also we have to check whether they are equal or not,
Consider(fog) (x) = f (g (x))
= f (√x)
= √x2
= x
Now consider(gof) (x) = g (f (x))
= g (x2)
So, (fog) (x) = (gof) (x), ∀x ∈ R+
Hence, fog = gof