Let ƒ: R → R and g: R → R be of the form f(x) = ax + b and g(x) = cx + d where a, b, c and d are constants. Determine necessary and sufficient conditions on the constants a, b, c and d so that fog=gof

Q: Find f.(x.y), f,(x,y), f.(1,3), and f,(-2,4) for the given function. If z = f(x,y) = 3x³y² – x²y³ +…

A: We need to calculate the partial derivatives fx(x,y), fy(x,y),fx(1,3), fy(-2,4). The solution is…

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: 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: If f(x) ' (1 ) cos (x)

A: We have f(x)=xcosx. So,            f'(x)=xcosx'            =xsecx'            =x'secx+secx' x…

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

A:

Q: .Let f, g andh are three functions defined as below : f: R>Rf(x) = 4x² – 4, - g. R→R8 (x) = V-5x+…

A: Given  f(x) = 4x2-4g(x) = -5x+1h(x) = 2x-5   a) fog(x) = f(g(x)) = f(-5x+1) = 4-5x+12-4 =…

Q: d dx y' z' y" z"

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Q: Let A = {x, y} and B = {w,z}. Describe all relations from A to B. Indicate which of these are…

A:

Q: Use a formula to express w as a function of t if w - V4s + 5 and s- ef - 1.

A:

Q: 2 Suppose y is a function of x such that y * and y(4) = -3. Find y. |

A: The differential equation is given by y' = 2x                                   .......(1) Initial…

Q: 2. Let f(x) = 3x + 6 € Z7[x]. Find all associates of f(x).

A: The given function is fx=3x+6∈ℤ7x To find: the associates of f(x).

Q: a51 - Find ax2@y3 if f(x,y)-x.e z

A:

Q: Write down the first order and second order conditions for maximum and minimum of a function y =…

A: Given,  Function y = f(x1, x2, x3,  .  .  .  , xn). To find the first order and second order…

Q: Let u = (-8, 1, 2) and Vf(a) = (-9, -5, -3). What is the value of Du[f] (a)? Du [f] (a) = 数字

A: Given: u=-8, 1, 2, ∇fa=-9, -5, -3To find: Dufa