15. Show that if f: A- 1 f(GnH)=f(G) B and G, H are subsets of B, then f-¹(GUH)=f(G) Uf (H) and nf (H).

Q: 23. If f(5) = 4, fi(5) = –1, g(5) = 2, and g/(5) = -3, find h/(5) for each of the following…

A: Given:

Q: 15. Use the From question #13. Between what two years did attendance For both grades drop? double…

A: Given: Use the double line graph from question #13. Between what two years did attendance for both…

Q: Show that the equation Fu 1 u 0x² ² 3t² 0 is satisfied by u=f(x+ct) + F(x-ct) where fand F are…

A:

Q: 5. Let f(x) = x² + 3x and g(x) = 2-x. (a) Find (f - g)(x) (b) Find (fg)(2) (c) Find (4) (x) and its…

A:

Q: Let f(x) = (x-9)7 – 8, determine f¯¹(x). - ƒ¯¹(x) =

A: To find the inverse of the function f(x) = (x - 9)7 - 8, we need to express x in terms of y, where y…

Q: Let f(x)=xsinx+V1-x Evaluate f'(-). Select one: а. 2 b. 0 C. d. 3

A: According to product rule of differentiation and according to power rule of differentiation .

Q: The functions f₁(x) = x² and f(x)=x³ are orthogonal on the interval [-3,3] ? True False

A:

Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

A:

Q: a+5 If f(z) = 3z-5 and g(z) = 3 %3D (a) f(g(z)) = (b) g(f(z)) = %3D (c) Thus g(z) is called an…

A:

Q: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: A 1. What is (go f)(x) if f(x) = 2x + 3 and g(x) = ? %3D O (go )(z) = + %3D O (go f)(x) = + } %3D O…

A:

Q: Find f'(x) for each of the following:< Ax) = 3x³ – 2x +4 b Ах) — 3(х + 2)? -2е a 8x* – 3x Ax) = Ax)…

A:

Q: of Find (7,- 2) if f(x,y) = 4x² + 7xy - 3y? + 6x - 5y - 2. of (7,- 2) = (Simplify your answer.)

A:

Q: Let f(x, y) /150- 4а2 — 2у? 4x? – 2y? Evaluate f(1, 3)

A:

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Let f(x, y, z) = x³ + 5x²yz + 3xz+ 3, v = Then: D, f(a) = 201 0 -2 and a = -5 2 -5

A: Given that f(x, y, z) =x3 +5x2 y z +3xz+3 The directional derivative is a concept from multivariable…

Q: Q21) One of the following is correct for functions the f(x)=1,g(x)= x³ and h(x) = ln(x): a) f(x),…

A: To check the linear independence we shall find the Wronskian for the given three functions. To find…

Q: Evaluate |(a,b)=(0,0) given that f(x, y) = 3x² + [y]; x = e²a+b₁ e²a+b; y = a² + t² + 1 да

A:

Q: Suppose a firm's technology is represented by the production function f(L, K) = min(L, 2K), where L…

A: As we know that all isoquant curves are strictly negative sloped hence, if one of the point is (4,…

Q: f(x+h)-f(x) 2. Evaluate h If a. G) f(Vx) b.

A:

Q: 119. If f(x) = a*, show that f(A + B) = f(A) • f(B).

A: Given: fx=ax For finding fA+B, we put x=A+B in given expression and simplify it

Q: Find Vf(a), given the following data. 91 Calculate 91, 92 and 93 such that Vf(a) = 92 93. 91 92 93 =…

A:

Q: of of and ду Find f(x,y) = Vx + 3y?

A:

Q: 4. Let f-(x) = g(x) = x-5, k-1(10) + 7 = 10 and h(x) = then find: b. Domain of h(x). c. (hof)(2). (Z…

A:

Q: Rx) = 3* f(x) = 3* -4 -2 2 4 y y 10 10 5. -4 2 4 2 -5 -5 - 10f - 10 y y 10 10 -4 2 2 4 -4 -2 4 -5 -5…

A:

Q: Let a, b 0. Find f(100) (a) provided that x³ (a - bx)²* f(x) =

A:

Q: 3. State the domain and range of f(x) = –- 2 D:(-x,0] А. D: В. D:[-2,0) C. D:[1,0) D. R:(-0,-1]…

A: To state the domain and range of,fx=-12-x-1

Q: 9) Find a linear function of the form f(x) = ax +b that satisfy the conditions A-4) = 8 and (3) - 9.

A: f(x) = ax+bf(-4) = 8→ -4a+b = 8.........................1f(3) = 9→3a +b =…

Q: Find the derivative. 1) f(x)= V7,7x A) 7.7)4/5 B) 7.7)-1/56 ,7) D) 2) y = x/10x-8 15x-8 A) 15x B)…

A: 1) Obtain the derivative of f as shown below: f'x=ddxx7+7x5       =15x7+7x-45ddxx7+7x…

Q: If f(1) = 4, f(2) = 3, f(3) = 1, and f(4) = 2, then what is f-1(3)? What is f(f-1(1))? What is…

A: Given : f1 = 4f2 = 3f3 = 1f4 = 2

Q: Two functions f, g are defined as follows: Find a) ƒ-¹(2) b) (gof)(-4) f(x) = 3x + 5 g(x) = 2(1-x)

A:

Q: Let f(x, y) = Evaluate f(5,5) 175 - 3x² - 4y2

A:

Q: 2. State the domain and range of f(x) ==Vx +2 5 D:[-2,0) D:[-2.) В. D:(-0,00) C. D:[0,0) D. R:(-0,0)…

A:

Q: 1. The functions fi(x) = 4x, f2(x) = x² + 6x, and fз(x) = 4x² + 12x do not form a linearly…

A: Step 1:  Step 2: Step 3: Step 4:

Q: Consider the function f(x) = 2x - 1/ x+3…

A: