Function f has the features described below fx is increasing

Function f has the features described below:

f(x) is increasing on interval (1,3)

f(x) is an even function

Tell whether each statement must be true, cannot be true, or might be true.

a) f(abs value x) is increasing on interval (-1,-3)

b) g(x)= -f(x) is concave up on interval (1,3)

c) f(x+1) is decreasing on interval (-4,-2)

Solution

Answer :

Function f has the features described below:

f(x) is increasing on interval (1,3) then for any a,b in ( 1 , 3 )such that a b implies that f(a) f(b)

f(x) is an even function then for any x in ( 1 , 3 ) such that f( - x ) = f( x )

a) Since if x < 0 we know that l x l = - ( x )

Hence f( lxl ) = f( - x ) = f( x ) is increasing on interval (-1,-3)

b) Let g( x ) = - f( x ) then g(x) is concave down on the interval ( 1 , 3 )

c) f(x+1) is increasing on interval (-4,-2) as f is even