Let A={x e R|-1sx s1} = B, Show that f:A →B given by f (x)=x|x| is a bijecti on.

Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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Q: Let R={(x,y) ERxR: |x| = |v|). Then R a function on R. оо True False

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Q: Let f e E(0, ox) and let a be a positive real number. Define the function fa as follows Sal) = {";…

A: Properties of Laplace transformation

Q: 3. Find the domain of the following functions: a.) f(x) = V1-x Inx b.) f(x) = Vx - 1lr

A: solutionsince the given (3)(c)f(x)=1-xlnx(b) f(x)=x-l ln(x)use have to find the domain of the…

Q: Let f : X → Y and g : X → Z be two bijective functions. Is the function h: X → Y × Z defined by h(x)…

A: Given: f:X→Y and  g:Y→Z be two bijective functions. To Check: Whether the function h:X→Y×Z defined…

Q: Let f = {(1,1), (2,3), (0, –1), (–1, –3)} be a linear function from Z into Z. Find f(x)

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Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: Let f : R → R be a function defined by f(x) = Decide whether it is an injection, a surjection, 1+ x2…

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Q: Identify an inner function (call it g) of y = (5x + 4)3.Let u = g(x) and express the outer function…

A: y=(5x+4)3

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

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Q: A = [a,b), be an (right half-open) interval of R. 6 (c) (d) a,be R+,b+00, Explain whether f(A) is…

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Q: 3. If f:(X,r)(Y.A) and g:(Y,A)→(Z,r) are open functions, prove that gof :(x.r)(Z.r) is open…

A: Definition: An open map is a function between two topological spaces that maps open sets to open…

Q: Let f(2) = z2 + 2|2|2 + z where f is differentiable. Determine the set of all points zo where f is…

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Q: (c) Evaluate the Riemann integral ₁¹(x) dx by using definition with the parti- tion 2n=1,2}, n+1 =…

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: 2. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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Q: Let (t) , a) Find the domain of F(t) b) Find " (t)

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Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…

Q: fex)= J4-x +2

A: The function is given by f(x) = 4-x + 2 To evaluate : The graph of the function f(x)

Q: Let f : R → R be defined as                   f(x) = 10x + 7. Find the function            g : R → R…

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Q: dA XB d(AXB) = Ax dB mp np %3D np Prove that where A and B are differentiable functions of u

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Q: Show that the function f : R → R given by f(x) = x3 is injective.

A: To show the given function is injective(one-one), first calculate the value of function at two…

Q: Let f (z) = ² + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

A: Real part of complex number

Q: Suppose f is a differentiable function on an interval II and f(x) 6= 0 for every x in the interval.…

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Q: Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

A: Given vector funtion and

Q: Let S(x²+2x)², x> 1, f(x) = Tax+ bx², ах x< 1. Compute for all a and b such that the function f(x)…

A: Proceed as shown

Q: Let f be the function from R to R with f (x) = x2. Is f invertible?

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