Question

Let f : R → R be defined as f(x) =10x + 7. Find the function g : R →R such that gof = fog = I_R.

Answer 1

∵ gof = fog = IR 

⇒ fog = IR 

⇒ fog(x) = I (x) 

⇒ f (g(x)) = x [∵ I(x) = x being identity function] 

⇒ 10(g(x)) + 7 = x [∵ f(x) = 10x + 7]

⇒ g(x) = (x - 7)/10

i.e., g : R → R is a function defined as g(x) = (x - 7)/10