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

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

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

Answer»

∵ 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