Let f : R → R : f(x) (2x - 3) and Show that (f o g) = I R = (g o f).

Question

Philoid · Accepted Answer

To prove: (f o g) = I_R = (g o f).

Formula used: (i) f o g = f(g(x))

(ii) g o f = g(f(x))

Given: (i) f : R → R : f(x) = (2x - 3)

(ii)

Solution: We have,

f o g = f(g(x))

= x + 3 – 3

= x

= I_R

g o f = g(f(x))

=

= x

= I_R

Clearly we can see that (f o g) = I_R = (g o f) = x

Hence Proved.