Let f ( x ) and g ( x ) be two piecewise functions that are defined as f ( - Maths - Relations and Functions

Question

Let f ( x ) and g ( x ) be two piecewise functions that are
defined as f ( x ) = { x2 , when x belongs to [ 0 , 2 ]
or 2 x ,when x belongs to [ 2 , 5 ] } and g ( x ) = { x2
, when x belongs to [ 0 , 3 ] or 2 x belongs to [ 3 , 5 ] } Show
that f is a function and g isn't a function

Vipin Verma · Accepted Answer

A function is valid when it is defined for all the value of x , it
means every f(x) has some value
And for a single x , we do not have two f(x)

So here we will check the condition
Let take f(x) case ,
We have
At , f(0) = 0 , f(1) = 1 , f(2) = 4 , f(3) = 6 , f(4) = 8 , f(5) =
10
Here we can see that all x value are valid for f(x) and at each x
there is different value of f(x) , hence it is a function

Lets take g(x)

At g(0) = 0 , g(1) = 1 , g(2) = 4 , g(3) = 9 and g(3) = 6 , g(4) =
8 , g(5) = 10
So here at x = 3 , we have two g(x)
Hence it is not a function

Let f ( x ) and g ( x ) be two piecewise functions that are defined as f ( x ) = { x2 , when x belongs to [ 0 , 2 ] or 2 x ,when x belongs to [ 2 , 5 ] } and g ( x ) = { x2 , when x belongs to [ 0 , 3 ] or 2 x belongs to [ 3 , 5 ] } .Show that f is a function and g isn't a function .

Let f ( x ) and g ( x ) be two piecewise functions that are defined as f ( x ) = { x², when x belongs to [ 0 , 2 ] or 2 x ,when x belongs to [ 2 , 5 ] } and g ( x ) = { x², when x belongs to [ 0 , 3 ] or 2 x belongs to [ 3 , 5 ] } .Show that f is a function and g isn't a function .