CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If f:AB and g:BC are onto functions, then show that gf is an onto function.

Open in App
Solution

f:AB and g:BC are onto. ......... [ Given ]
Then, gf:AC

Let us take an element z in the co-domain.
Now, z is in C and g:BC is onto.
So, there exists some element y in B, such that,
g(y)=z ---- ( 1 )

Now, y is in B and f:AB is onto.
So, there exists some x in A, such that,
f(x)=y ----- ( 2 )

From ( 1 ) and ( 2 ),
z=g(y)=g(f(x))=(gf)(x)
So, z=(gf)(x), where x is in A.
gf is onto.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon