3. Let f: A→ Band g: B → Cdenote two functions. Show that if gofis 1-1, then fis 1-1. D JCI

Q: Let f : R R:f(x) = 10x + 7. Find the function g : R→R such that gof = fog = IR. %3D %3D

A: Given f: R -> R  such that f(x) = 10x + 7 and  g : R -> R such that g o f = f o g = IR

Q: 3. Let f(x) = x² + 3 and g(x) = Vx – 3 be functions defined on [0, ∞) and [3, 00), respectively. i.…

A: According to question,  Given functions, f(x) = x2+3, g(x) = x-3 Function fx defined on interval :…

Q: Question 1. Suppose A = {a, b, c}. Let f : A → A be defined by f(a) = c, f(b) = a and f(c) = b.…

A: The function f is an inverse of g or g is an inverse of f if fog=I and gof=I.

Q: For which values of a ∈ R is the function f(x + iy) = (a2x - axy) + i(- ax2/2 + ay), an entire…

A:

Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: Let A E RDXE, XE REXF, B € RFXD. Computed where g(X) = tr(AXB).

A: Let A∈ℝD×E, X∈ℝE×F,   B∈ℝF×D To Compute ∂g∂X where g(X)=tr(AXB)

Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

A:

Q: a. Let X = {2, 4, 6} and Y = {a, b, c, d'}. Define g : X→ Y by the following arrow diagram. X 2 4 bo…

A:

Q: Let f(x, y, z) = 9xy sin (yz) and F = Vf. Evaluate F · dr, where C is any path from (0, 0, 0) to (5,…

A:

Q: Prove that there is an additive function T : R --> R that is not linear.

A: Let T: V→W  be the linear transformation and we it is linear,…

Q: 3. Let f: A-→ B and g : B A be functions. Suppose that y = f (x) if and only if r =g (y). Prove that…

A:

Q: 4. Show that if f and g are pdfs and a € [0, 1], then af + (1-a)g is also a pdf.

A: Given that  Show that if ƒ and g are pdfs and α [0, 1]  then αf + (1 -α )g is also a pdf.

Q: Let E = {0, 2, 4, 6, ...}, define ƒ: E × E → Z¹ by the formula f(m, n) = 4m5¹, \ (m, n) € Ɛ × Ɛ.…

A:

Q: For any subset A of R, define the function XA : R →R by if x E A 1, XA(") = 0, if x ¢ A. Let A and B…

A:

Q: sst. Let f(x, y, z) = x³ yª + zª and x = s5, y = st³, and z = s

A:

Q: e equation of

A:

Q: Let F ____ {(a, b]: a, b E Q). Show that a(F) = B(R).

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: 4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that {f(x) EYE A}, and…

A:

Q: 2. Let g (x, y) = 2x² – y² . Compute 9(1, 2), g (2, 1), g (1, 1), g (–1, 1) and g (2, –1).

A:

Q: b) Let f: D→ C be a function and Y a subset of C. Show that f¹ [C-Y] =D-f¹ [Y].

A:

Q: 15. Let A = {0, 1, 2, 3) and define functions F and G from A to A by the following formulas: For all…

A: Given: The set A=0,1,2,3 and the functions Fx=x+42 and Gx=x2+3x+1, for all x∈A To determine: Whether…

Q: Let f(x.y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 Oc. 0 Od.-2 e. 2

A: From the given problem:   fx,y=lnx2y   fx2,1=fy5,a   Now,   fx=∂f∂x=∂ ∂ xlnx2y=1x2y∂ ∂ xx2y=1x2y·…

Q: 18. Let A = {1,2, 3}, B = f: A → B, and g : B → C, such that {W, Y, Z}, C = {7, V2, V5}. Find…

A:

Q: 10. Let F(x, y, z)= y-yz+1 £z+r-z z+xy-y Find a function g such that F = √g.

A:

Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

A:

Q: 10.18. Let A = {w, x, y, z} and B= {r, s,t}.Give an example of a function f: A →B that is neither…

A:

Q: Given, F = x²yî – 2xzj + 2yzk. Find V × (V × F)

A:

Q: Let f(x, y) = x for y=0 and 0 for y+0. Evaluate each of the following or if they do not exist, state…

A:

Q: 8. Find a function g such that og = 2² - sinz. Əz 9. Find a function h such that Əh əz 10. Find a…

A: 8. Given that ∂g∂z=zz2-sin z. We have to find a function g that satisfies the given condition. Note:…

Q: a)Suppose f: R → Z, where f(x) = [x + ¹] i. Graph the function f(x). ii. If A = {x: 1 ≤ x ≤ 3}, find…

A:

Q: 2. (8.7.10) Let f (x, y) In y R is the rectangle defined by R {(x, y)|1 < x < e2 and 1 < y < e}.…

A:

Q: {4, X, {m}, {n}}. [0, 0) by Q. Let X = {m, n}, and = %3D Define the function um : 2 if me A then…

A:

Q: Exercise 2. Let f : A → B be a function with Y1 and Y2 subsets of B. Prove that if Y1 C Y2, then…

A: Let f:A→B be a function and let Y1,Y2⊆B. Suppose that Y1⊆Y2 To show f-1(Y1)⊆f-1(Y2) Let x∈f-1(Y1)…

Q: Let f(x.y) = In (x³y) . If f(6,2)=f,(5,a) what is the value of a? O a 1 O b. -1 Oc. 0 Od. 2 O e. -2

A: