Let f: Z → Z be given by S2x – 1 if x is even if x is odd f(x) = 2x a.) For S = {0,1, 2}, find f(S) and f-'(f(S)). b.) For T = {-1,1,4}, find f¯'(T) and f(f¯²(T)).

Q: 9.) Consider the function f (x) = x? – 2x – 1 for x € [2,4]. Use n = 10 to compute accurate to 10…

A:

Q: Let f(t) = 3t4 - 6t+ 3et. Then f'(t) =

A: To find f'(t)

Q: Suppose that f (0) = 2 and f'(x) 0. Show that f(4) 0.

A: f(0)=2   and f'(x)≤3  for all x>0 ⋯(i)integrate (i) w.r.to x ,we getf(x)≤3x+kput…

Q: prove the following relationships. Note that x(z) = ] [x(+)]. 1. ] [ a^² XLE)] = x ( ² / ) 2. ] […

A:

Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f,(x,y) =, %3D B) f,(x, y)…

A: Power role of derivative: ddxxn=nxn-1 Derivative of function eax: ddx(eax)=aeax Given function is…

Q: Suppose that f'(x) = 2x for all x. a) Find f(4) if f(0) = 0. b) Find f(4) if f(2)= -1. c) Find f(4)…

A: Given f'( x ) = 2x

Q: dz 2 = -ry", where r = st“ and y = –st". Compute – as a function of s and t only evaluate this when…

A:

Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: L=2-36X, y'co) =5, and ylo)=S x)

A:

Q: 8. For the function y = e* + sinx: a. Determine y', y",y",y^),y(5), y(6). b. Describe the pattern…

A: We have to find the differentiations of the give function and find y101.

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

A:

Q: find all pairs (m, n) of positive integers such that ϕ(ϕ(n^m)) = n, where ϕ(n) is Euler's totient…

A:

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

Q: F(f)= 2 x-3 4x+1 a Find the dom F and dom F b-) Find ran F and ran F'

A:

Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

A:

Q: For f(x1, x2) = x2 cos x1 find f'(x1, x2), f'(2,7) and df[(2,7); h]. For f(x, y, z) = (x – 2z)e"…

A:

Q: Let f(x) = 5- x and g(x) 2, find: a. (fog)(0) b. (go f)(0) = c. (fo g)(x) Preview d. (go f)(x) =…

A: Value of the above ques is

Q: OD Findof the following functions: 1) e" = In(x²y) – y² + 2x* 2) y t = (2x – 3)²

A: Find the derivative of the following function

Q: Let 11 f(x) = ( – 2a² – 4)(7z² – 4)" - - f'(x) =

A:

Q: Any function of the form f(x, y) = ax*y" where a is a real number and k, n are positive integers…

A:

Q: Find the domain of Hi function fr w =J 2x+3 -1

A: It is given that the function fx=2x+3-1. Find the domain of the function. It known that the root of…

Q: The domain of f(r) =tan(x) is Select one: a. 2 2 O b. IR - + nn} O c. IR O d. R {nt}

A:

Q: Let f(x)= x³+1. Then (fof)'(1)= O 20 O 36 O 3 O 9

A: Please refer to the image below

Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).

A: X~Gammar,λ fx=λrΓre-λxxr-1,     x>0, r>0, λ>0 Y~Gammas,λ fy=λsΓse-λyys-1,     y>0,…

Q: Determine whether f is a function from Z to R if a) f(n) = tn. b) f(n)=√√n² + 1. c) f(n) = 1/(n² —…

A: Function: Let f:M→N be a function, then every element of set M has one and only one image in set N.

Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

A:

Q: Let f(2) = (32² – 7)* ( – 7æ² + 8)² f'(x) =

A:

Q: Find y as a function of a if y(0) = 12, y(0) = 21, y"(0) = 18. y(x) = y" 16y" +63y = 144e²,

A: Given: y'''-16y''+63y'=144ex y0=12 y'0=21 y''0=18 To find: Solution to the given differential…

Q: x -x-2 Find f"(3) if Ax)- x-2 O a) 1 O b) -1 O c) 2 d) -3

A: using quotient rule