Let h be a convex decreasing function and g a convex function. Is it true that h(g(x)) is a quasi-concave function?

Eliza Gregory 2022-10-25 Answered
Let h be a convex decreasing function and g a convex function. Is it true that h ( g ( x ) ) is a quasi-concave function?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

periasemdy
Answered 2022-10-26 Author has 15 answers
Yes.Since g is convex, for λ [ 0 , 1 ] ,,
g ( λ x + ( 1 λ ) y ) λ g ( x ) + ( 1 λ ) g ( y ) .
and
λ g ( x ) + ( 1 λ ) g ( y ) max [ g ( x ) , g ( y ) ]
Since h is decreasing,
h [ g ( λ x + ( 1 λ ) y ) ] h [ λ g ( x ) + ( 1 λ ) g ( y ) ] h ( max [ g ( x ) , g ( y ) ] ) min [ h ( g ( x ) ) , h ( g ( y ) ) ] .
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-10-29
Consider a function f : [ 0 , 1 ] R + such that f ( 0 ) = 0 and f ( x ) f ( y ) for all x y (i.e f is monotone).Is a positive, monotone and sub-additive function concave?
asked 2022-11-05
Show that the function:
f ( t ) = log det Z i = 1 n log ( 1 + t λ i ) trace ( ( Z + t V ) 1 Y )
is concave in t.
asked 2022-10-22
Suppose we have a system of equations:
x 1 = f 1 ( x 1 , . . . , x n ) x 2 = f 2 ( x 1 , . . . , x n ) . . . x n = f n ( x 1 , . . . , x n )
where the f i are components of the gradient f for a monotone increasing, concave function f, so f i > 0 and f i x i 0.
Does the system of equations necessarily have a solution? And is it unique if it exists?
asked 2022-11-07
What this means: Hence, v(6,000) < v(4,000) + v(2,000) and v(-6,000) > v(-4,000) + v(-2,000). These preferences are in accord with the hypothesis that the value function is concave for gains and convex for losses
asked 2022-11-22
Given a C 2 L-smooth function the Lipschitz condition is:
| | f ( x ) f ( y ) | | L | | x y | |
Are these conditions only true for convex C 2 function? What will change If f is C 2 and concave?
asked 2022-11-16
How to show that the entropy H ( Pois ( λ ) ) of a Poisson distribution Pois ( λ ) is Concave in parameter λ? i-e
asked 2022-11-11
If linear function is convex or concave? For example f ( x ) = x, is function whose second derivate is 0 so we cant tell anything using this criteria.

New questions