7. Before we formulate the problem make one reminder: A function f is quasiconcave if and only if for every a and y and every A with A € [0; 1], if f(r) ≥ f(y) then f((1-A)r + Ay) ≥ f(y). Suppose that the function F is quasiconcave and the function g is increasing. Show that the function f defined by f(x) = g(F(x)) is quasiconcave.

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

A:

Q: 3. Let h(x) = (f og)(x). Given f(x) = 3x2 +5 and g(x) = Vx – 3. a. Evaluate h(4). b. Determine fx).

A:

Q: Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) =…

A: Big-Θ notation: A function g(n) is in Θ(f(n)) if there exist constants c1, c2, and N such that…

Q: Suppose f is a function of two variables with the property that f(−x, y) = − f (x, y) for all values…

A: Given Information: is a function of two variables such that  for all values of x and y.To find: The…

Q: The functions f(x) and g(x) are graphed on the set of axes below. XA 1(x) g(x) For which value of x…

A:

Q: If you have a function with a discontinuity, is it still possible to have f′(c)(b−a) = f(b) − f(a) ?…

A: Consider a piecewise function  f(x)={1, x≠1             0, x=1} over the interval [0,2] In the given…

Q: 4. Let function f: R → R and function g: R → R be two functions for which f(g(x)) = x and g(f(x)) =…

A: We have to prove given statement.

Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

A: Let               f1 : X→Y , f2 : X→Y be two functions, then we say that the functions f1 and f2 are…

Q: 1. Write the domain of the following functions and draw a corresponding picture. f(x, y) = In(y-x)…

A: To find the domain of the function  f(x,y)=y−x2ln(y−x)​, we need to identify the values of ( x ) and…

Q: 4. If the function f(x) is defined by f(x) =-6 then which of the following is the value of f(10)?…

A: We solve using substitution

Q: 16. Given f(x) = 2* + 2, g(x) = x² − 1, and h(x) = 2x, determine an algebraic and a graphical model…

A: Since you have posted multipart question i can do first three subparts as per our company guidelines…

Q: Suppose we have a function defined by f(x)={2for x>1,xfor x≤1. What is the value of f(1) ?

A:

Q: 1. Given f(x) is a one-to-one function with Df: [4,25] U (42,100] and Rf: (-o,-14], find the domain…

A:

Q: 7. Determine each of the following for the function, f(x, y) = 7x³y² - 2x + 3y. Show all work toward…

A: Given,  f(x,y)=7x3y2-2x+3y

Q: - If f(x) = x + 6 and h(x) = 7x – 2, find a function g such that g 。 f = h. °

A: