# Let f: R → R be defined as f (x) = 10x + 7. Find the function g : R → R such that g o f = f o g = 1R.

It is given that f: R R be defined as f (x) = 10x + 7

Let f(x) = f(y), where x, y ϵ R.

10x + 7 = 10y + 7

x = y

f is a one – one function.

For y ϵ R, let y = 10x + 7.

x = Therefore, for any y ϵ R, there exists x = such that f is onto.

f is an invertible function.

Let us define g : R R as Now, we get:

gof(x) = g(f(x)) = g(10x + 7) And, gof = IR and gof = IR

Therefore, the required function g : R R is defined as .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Functions - 0152 mins  Different kind of mappings58 mins  Functions - 0648 mins  Functions - 1156 mins  Quick Revision of Types of Relations59 mins  Range of Functions58 mins  Some standard real functions61 mins  Battle of Graphs | various functions & their Graphs48 mins  Functions - 0947 mins  Quick Recap lecture of important graphs & functions58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 