Q. 85.0( 2 Votes )

Let f: R R an g: R R be defined by f(x) = x + 1 and g(x) = x 1. Show that fog = gof = IR.

Answer :

Let f: R R and g: R R are defined as


f (x) = x + 1 and g (x) = x – 1


Now,


fog(x) = f(g(x)) = f(x – 1) = x – 1 + 1


= x =IR ……(i)


Again,


fog(x ) = f(g(x)) = g(x + 1) = x + 1 – 1


= x = IR ……(ii)


from (i)& (ii)


fog = gof = IR


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