Q. 95.0( 2 Votes )

Verify associativity for the following three mappings: f: N Z0 (the set of non – zero integers), g: Z0 Q and h: Q R given by f(x) = 2x, g(x) = 1/x and h(x) = ex.

Answer :

We have, f: N Zo, g: Z0 Q and h: Q R


Also, f(x) = 2x, and h(x) = ex


Now, f: N Zo and hog: Z0 R


(hog)of: N R


Also, gof: N Q and h: Q R


ho(gof): N R


Thus, (hog)of and ho(gof) exist and are function from N to set R.


Finally. (hog)of(x) = (hog)(f(x)) = (hog)(2x)



Now, ho(gof)(x) = ho(g(2x)) = h



Hence, associativity verified.


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
Functions - 10Functions - 10Functions - 1047 mins
Functions - 05Functions - 05Functions - 0558 mins
Functions - 07Functions - 07Functions - 0748 mins
Inverse Trigonometric Functions - 01Inverse Trigonometric Functions - 01Inverse Trigonometric Functions - 0161 mins
Range of FunctionsRange of FunctionsRange of Functions58 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