The function f is defined by f(x) = {(x^2,0<=x<=3) ; (3x,2<=x<=10)}.
The relation g is defined by g(x) = {(x^2,0<=x<=2) ; (3x,2<=x<=10)}.
Show that f is a function and g is not a function.
The relation g is defined by g(x) = {(x^2,0<=x<=2) ; (3x,2<=x<=10)}.
Show that f is a function and g is not a function.
Answers & Comments
Step-by-step explanation:
The relation f is defined as f(x)={
x
2
,0≤x≤3
3x,3≤x≤10
It is observed that for 0≤x≤3, we have f(x)=x
2
and for 3≤x≤10, we have f(x)=3x
Also at x=3, f(x)=3
2
=9 or f(x)=3×3=9
i.e., at x=3,f(x)=9
Therefore for every x, 0≤x≤10, we have unique image under f
Thus, the relation f is a function.
Also, the relation g is defined as g(x)={
x
2
,0≤x≤2
3x,2≤x≤10
It can be observed that for x=2, we have g(x)=2
2
=4 and g(x)=3×2=6
Thus, the element 2 of the domain of the relation g has two different images i.e., 4 and 6
Hence, this relation is but not a function.