Q. 75.0( 3 Votes )

Let f: R R and g: R R be defined by f(x) = x2 and g(x) = x + 1. Show that fog ≠ gof.

Answer :

We have, f: R R and g: R R are two functions defined by


f (x)= x2 and g(x) = x + 1


Now,


fog (x) = f(g(x)) = f(x + 1) =(x + 1)2


fog(x) = x2 + 2x + 1 ……(i)


gof(x) = g(f(x)) = g(x2) = x2 + 1 ……(ii)


from (i) & (ii)


fog ≠ gof


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 01Functions - 01Functions - 0152 mins
Inverse Trigonometric Functions - 01Inverse Trigonometric Functions - 01Inverse Trigonometric Functions - 0161 mins
Range of FunctionsRange of FunctionsRange of Functions58 mins
Functions - 10Functions - 10Functions - 1047 mins
Functions - 05Functions - 05Functions - 0558 mins
Functions - 07Functions - 07Functions - 0748 mins
Functions - 02Functions - 02Functions - 0253 mins
Functions - 03Functions - 03Functions - 0361 mins
Functions - 08Functions - 08Functions - 0840 mins
Functions - 12Functions - 12Functions - 1252 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
caricature
view all courses