If fx=x-1 and gx=fffx the value for x>2,g'x=
1 for all x>2
1 for 2<x<3
-1 for 2<x<3
Not defined
Explanation for the correct option:
Finding the value of g'x:
Given that,
fx=x-1
For x>2
Now,
ffx=fx-1=x-1-1=x-2
fffx=fx-2=x-2-1=x-3
gx=fffx=x-3
For x>3,
gx=x-3
and for x<3
gx=-x-3=3-x
Differentiate the above function with respect to x.
g'x=1andg'(x)=-1
Here, g'x=-1 satisifes the conditon 2<x<3.
Hence, the correct option is C.
Use the factor theorem to determine whether g(x) is a factor of f(x)
f(x)=22x2+5x+2;g(x)=x+2