Define a function g(x) of a random 1; if x2x, 0; otherwise variables by g(x) = %3D Where x, is a real number – o< X, <∞ Show that E [g (X)] = 1-F, (x,) >

Q: Consider the function f(x) where. 2x²-x +3. if x>2 jf x=2 if x<a f(x) = 4 4-X Is the function…

A: Solution:

Q: Find the local minima/maxima of -x + ln x if it exist

A: fx=-x+lnx Differentiating with respect to x, we get f'x=-1+1x Now to find critical values, solve the…

Q: Let f(x) = 6x² + 2x³. Select all intervals where f(x) is INCREASING, (3) (0, ∞) (,0) (-∞, -3¹²¹)

A:

Q: Let f(x) = { *, if x= 2 ; for the eax if x + 2 function to be continuous at x = 2 the value of a is

A:

Q: Let x + 1 f(x) x + 9 f-'(- 4) =

A: To find the solution first we have to find the inverse of the given function and then evaluate it at…

Q: For what value of k will the function f be continuous on (-, ∞)? x2 - 81 if x + -9 f(x) = X + 9 k if…

A:

Q: 1 show that f (-2) = f(2). 4 If ƒ(x) = x" 4

A:

Q: f(x)= 23-4b            If x=3

A: Continuity: A real function f(x) is said to be continuous at a∈R (R− is the set of real numbers), if…

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

A:

Q: Which of the following are generally NOT true, for any given function f:X-->Y and subsets A and B of…

A:

Q: Let f(x) = 5x and g(x) = ex + 7. Determine the x-coordinate where the graphs of the two functions…

A:

Q: let H(x)(1+x^2)^3. find f and g such that f(g(x))=H(x)

A:

Q: Q3\ a) Find the values of a and b to make the functions continuous at every x: ax + 2b 2) g(x) = }x²…

A: Given function is,  f(x)=-2        ;x≤-1ax-b   ;-1≤x≤13          ;x&gt;1