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 = I_{R}.

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 =I_{R} ……(i)

Again,

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

= x = I_{R} ……(ii)

from (i)& (ii)

fog = gof = I_{R}

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