when x = 2
g(2) = 4 and g(2) = 6 , two different values of g for one value of x. That is a no no.
however f(3) is just fine, 9 for both coming from below and coming from above
The relation g is defined by g(x)={x²,0<=x<=2,3x,2<=x<=10
Show that f is a function and g is not a function.
Plz help me sooon
g(2) = 4 and g(2) = 6 , two different values of g for one value of x. That is a no no.
however f(3) is just fine, 9 for both coming from below and coming from above
For the first part of the definition of f(x), f(x) = x² for the range 0≤x≤3. In this range, every input value has a unique output value since squaring a number always gives a unique result.
For the second part of the definition of f(x), f(x) = 3x for the range 3<x≤10. In this range, again, every input value has a unique output value since multiplying a number by 3 also gives a unique result.
Therefore, f is a function because for any given x value within the specified ranges, there is only one corresponding y value.
Now, let's evaluate g to determine whether it is a function or not.
For the first part of the definition of g(x), g(x) = x² for the range 0≤x≤2. In this range, every input value has a unique output value, similar to the first part of f(x).
The issue arises in the second part of the definition of g(x), g(x) = 3x for the range 2<x≤10. In this range, several input values, specifically x = 2 and x > 6, will produce the same output value of 6. Therefore, there are multiple x values corresponding to the same y value, violating the condition for a function.
Hence, g is not a function as there exist x values with multiple corresponding y values, violating the uniqueness criteria for a function.
In summary:
- f is a function since each x value has a unique y value.
- g is not a function since there exist x values with multiple corresponding y values.