a) E(X), E(X²) and E[(X − 1)²] b) Var(X) and ox

Q: 3) Show that (f o g)(x) = (go f)(x) = x. f (x) = 4 – 3x g(x) = (4 – x)

A:

Q: 5) Given functions T(x) = 3x – x² and S(x) = 4x – 1 find the following: a) (T • S)(x) b) (T – 5)(-)…

A: Note:  In (T o S)(x) , s(x) is input. (T-S)(x) = T(x)-S(x).

Q: If f(x) = a* + 2, g(æ) = x – 7 and h(x) = Va, then f(g(h(x)))= Preview

A:

Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 2x + 1. 3 h(x) = /2x+1 f(x) =|

A: topic - functions

Q: S (x + ¹) ex x²+2x-3 dx

A:

Q: Find a formula for f (z) if f(z) = I+1 f '(z) =O ( )'(2) =D-

A: We will use concept of inverse function and differentiation of a function.

Q: If E[X]=−1E[X]=−1 and Var(X)=5Var(X)=5, then E[(3+4X)2]= and Var(2+5X)=

A: Given, E[X]=-1 Var[X]=5 Concept: E[Constant]=constant Var[constant]=0

Q: Find the domain of v. v (x) = x + ln(7x - 4)

A: Find the domain of v. v (x) = x + ln(7x - 4)

Q: Find a general formula for f("). f(x) = (x + 6)- (Use symbolic notation and fractions where needed.)…

A: Consider the provided question,

Q: Find h(x) and g(x) such that f(x) = (h o g)(x). f(x) = V3x +4 Suppose that g(x) = 3x+4. h(x) = %3D

A:

Q: If f (x) = ln x, then lim I-3 А B D In 3 nonexistent f(x)-f(3) is

A:

Q: If Var(X+Y) = 3, Var(X- Y) = 1, E(X) = 1, and E(Y) = 2, then E(XY) %3D 5/2 1/2

A: Solution: From the given information,

Q: How do you show that if f(x) is O(x), then f(x)=O(x2)?

A: Here we use the definition of big-O.

Q: are there any problems where (fog )(x)=(gof )(x)

A:

Q: 5. Show that the formula for the Secant method can be written in the form xn+1 = [f(xn)xn-1…

A: Secant Method: Consider, y = f (x). Let, x0 and x1 are two initial approximations for the roots of f…

Q: a) fo f(x) dx d) f3f(x) dx b) √²³ƒf(x)dx c) ff(x) dx e) fºƒ(x)dx − [f(−ƒ(x))dx + f² ƒ(x)dx]

A: Note:- according to the company policy we can attempt maximum three subparts of a question so please…

Q: Given  f(x) =  x  over  5 + x  and  g(x) =  5x over 1 − x,  complete the following. (a) Find…

A:

Q: Find a and b

A: Given that ∫621​f(x)dx−∫612​f(x)dx=∫ab​f(x)dx  This can be rewritten as…

Q: If f(x) = x* + 8, g(x) - = x – 4 and h(x) = Va, then - f(9(h(x)))-

A: