Let f : A → B and g : B → C be functions and let h = go f. If f and g are injective, then so is h. %3D

Q: Express the function in the form f • g o h. F(0) = Vsin3 0

A: We have to express given function in the form f•g•h

Q: Reduce the following function: Z = ((A© B)•(A•C) )•( (A•B) +(A © B) ) %3D

A: Given, z=A⊕B·A·C·A·B+A⊕B

Q: The following function is injective or not?  p : N × N → N, p(n, m) = n + m  t : Z → Z, t(n) = n −…

A: Given functions, i. p: N×N→N, defined by p(n,m)=n+m. ii. t: Z→Z, t(n)=n-2020. To check which of them…

Q: Find f'(x), f''(x), and flo (x) for the following function. f(x) = 2ex f'(x) = f"(x) =O %3D A3) (x)…

A: The given function is f(x)=2ex

Q: The set of functions S = span{e™" | n e Z} separates [0,1]). True False

A: S=span{enx |n∈Z}

Q: Evaluate the difference quotient for the given function f (a +h)-f(a) f(x)=x', h

A:

Q: Name an interval where the following function is non-linear. 4 5. 7 10 O 6 <x< 10 O 2 x<5 O 0 x< 2 O…

A: We know that , Graphically a linear function is a function whose garph is a straight line by…

Q: Let F: X Y and G:

A: Given: Let F : X→Y and G : Y→Z be the two non-constant holomorphic maps between Reimann surfaces.

Q: Differentiate the following function. r(t) = (5t",8 /t, r'(t) =

A: Given:rt=5t4, 8t , 9tDifferentiation formula:ddxxn=n.xn-1

Q: Find f'Ce) g function. of the following f (x) X5 %3D 5.

A:

Q: Place the values of f(a), f'(a), and f"(a) in increasing order. If the point appears to be a max or…

A: At x- axis value of f(x) is zero For positive slope f'(x) is positive And if graph is concave down…

Q: Assuming f and g are differentiable functions, determine ) (2) if f(2) = 5, f' (2) = -7, 9(2) = 8,…

A:

Q: Determine whether each of the following functions is (a) continous (b) differentiable. Show a…

A: Determine whether the function is a) continuous.b) differential.show a complete solution. 1.f(x)=…

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: 4. f(x) = 5. f(x) = at x = 2 %3D 一八 at x = 0 %3D

A: This is problem of continuity of the function.  Function is called as continuous if the right hand…

Q: Use the given function f to answer parts (a) through (f) below. f(x) = - 3+ In x

A:

Q: OShow that function fex)- xl îsnotalifferentible ato

A:

Q: Let f(x.y) = In ( x2 + y ). If f,(2,a)=f,(- 1, 2), what is the value of a? O a. 6 O b.3 O. 7 O d. 8…

A:

Q: Decide whether the composite functions, f ° g and g • f, are equal. ( that is: does fog return the…

A: Given: fx=x+1gx=x2 To Determine: Whether the composite function, fog and gof are equal.

Q: Let f be a function. Then f (a) + f (b) = f (a + b) . O True O False

A: We need to proveor disprove if  fa+fb=fa+b

Q: Let /: X→Y be a function, A, B C X and C, DCY. Show that: 3. If CSD then SF (D) 4. f¹(COD)=f-¹(C)…

A:

Q: Suppose that f and g are both odd. Which of the following functionsare even? Which are odd?(a) y = f…

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: Let µ* (E) =0 , then µ * (E U F) =µ* (F) ▼ F C R.

A:

Q: (e) If f and g are differentiable then, d -f(g(x)) = f'(g(x))g'(x) dx True False

A:

Q: Let f(x) = x"h(x). Given that h(-1) = 5 and h'(-1) = 8, calculate f'(-1).

A: fx=x11hx h-1=5 h'-1=8 we have to calculate f'-1

Q: Write the following as a composition of two or more non-identity functions. (g o n(x) = F(x) = (x² –…

A: Composite function: - A composite function is one that is dependent on another function. By…

Q: Assume that f(x) and g(x) are both differentiable functions. Given f(3) = -2, -4, f'(3) = 8, and…

A: Given that f(x) and g(x) are both differentiable functions and  f3=-2, g3=-4, f'3=8, g'3=2

Q: Let y = f(x) be the piecewise dehned -x- 1, if x <-2, f(x) = {1, if 2 < x < 2, 1, if x 2. - f(-3) =…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: For what value of the constant c is the function f continuous on ( 00, 00) where ( cb + 7 c(b)? – 7…

A: Given: fb=cb+7       if b≤6cb2-7   if b&gt;6 Here the given function is continuous at x=6 Therefore,…

Q: Let g(x) = = X-f(x) S(x) , find g'(1),if f(1) = 4 and f'(1) = 2

A: Given that g(x) = -x-f(x)f(x). We have to find the value of g'(1). Given that f(1) =4 and f'(1) =2.…

Q: Iff: X→Y is an injective function and A, BCX then: f(A-B) f(A)- f(B)

A: Use the concept of injection map of functions.

Q: Determine the domain and range of the function f: {r,s,t,u} ➔ {A,B,C,D,E} defined by f(r) = A, f(s)…

A: Domain of a function is the set of possible values of independent variable. The domain of given…

Q: Determine whether ? is a function from Z to R if a. ?(?) = ±? b. ?(?) = √?^2  +  ? c. ?(?) =1/(?2−4)

A: Solution:-

Q: Use this information to answer parts a and b. - express N as a function of t.

A:

Q: Let f : D → E be a function and let A C D, BC E. Prove the following: (a) f(f-1(B)) C B. (b) If f is…

A: The function is f:D→Eand A⊆D and B⊆E

Q: Consider the function f : A → B.

A: Given the function f : A→ B. The relation  f^ from ℙ(A) to ℙ(B) is defined by…

Q: Let f € C[a, b]. Suppose that for every [a1, b1] C [a, b], S f(x) dx = 0. Show that f(x) = 0, x E…

A:

Q: Find f', f'', f'"' and f (4) for the function. f(x) = x* – a³ – 9x- f' (æ) = Preview f''(x) =…

A: We have to find

Q: find the domain of the given function. f(x, y) = X-y %3D D=R2-{(a,-a)}AO D =R2-{(a,a)} .BO D=R -…

A:

Q: Find ao of the function f(x) =( – x)? %3D | O 5 T^2/6 5 T^2/12 O n^2/6 TI^2/12

A: Value of ao in the Fourier series

Q: Let f(x) = Find f'(x). Show your wor et + 2

A:

Q: If f(x) = æ“ + 3, g(x) = x – 5, h(æ) = Va, then fogo h(x)= Preview

A:

Q: Show whether or not the following function is coercive: f (æ1, æ2) = e*i + e*ž – a200 – ažº ,200 %3D

A:

Q: 7) S(x) = x\x|– x³

A: To find if the function is even or odd.

Q: x, 4x , 7x , 10x , 13x

A:

Q: Let f(x, y) = e*Yx4 Evaluate f(3, 5)

A:

Q: What is the domain of the function f(x) = VIn a ? %3D O le, 00) O 0, 7) O [1, 00) O -0, 00) O ( 0,…

A:

Q: Suppose f (x) = (e*)?. Evaluate: A (e*)²+c 글(e)2+ C В © 2(e*)²+C C (e")³ +c D

A:

Q: Find f(x) and g(x) such that h(x) = (f ∘ g)(x). (Use non-identity functions for f(x) and g(x).)…

A: The given functions,hx=f∘gxandhx=x6-500

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.