Given a function f : A → B. Define the relation f from P(A) to P(B) by f = {(X,Y) C P(A) × P(B)|Y = f(x)}. 1. Show that ƒ is a function from P(A) to P(B). 2. Show that if f is one-to-one, then f is one-to-one. 3. Show that if f is onto B, then f is onto P(B).

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A: Observe the given functions as follows.

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A: Given :  f(x) = x/x+1

Q: .Suppose f E S(R) is an even function. Show that f is also even and that

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Q: 1. Why is f not a function from R to R if a) f(x) = 1/r? b) f(x) = x? %3D

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A: Given y=f(x)=9x+1

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Q: The relation f = {(x, y) E R x R 3is x+1, 1. Not function 2. Function 3. On to function 4. One to…

A: According to our guidelines, we can answer only the first question, the rest can be reposted. Given…

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Q: Use the limit definition for the derivative to calculate f'(x) for each of the following if f'(x)…

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Q: 2. For each function f(x) given below, find the general derivative f'(x) as a new function by using…

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Q: Let g : R → R be a bounded function and define f : R\{0} →R by 1 f(x) = g(x)+ Using only the…

A: It is given that ;                f : R \ 0 →R  defined by     fx = gx + 1x2 Where,   gx  is a…

Q: Consider the function f(x) = {,* - a, -1<x< 2 lb – 2x, 2<x<4 If b =1 and the limit of f (æ) as æ → 2…

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Q: Let f(x)=x²+x. Compute f'(2) using the definition of the derivative, f(a+h)= f(a) f'(a)= lim h 0 h

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Q: Define functions f and g from R to R by the fol- lowing formulas: For every x E R, 2x° + 2x = 2x and…

A: It is given that, f(x) and g(x) are defined from R to R by the following formulas:

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Q: For real numbers m and b with m + 0, show that the map f: R-→ R defined by f(x) = mx + b is…

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A: To find f'(x) by definition f(x)=√(9-2x)

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A: We have to define which statement is wrong

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Q: So if rs0 1 if r>0 7. Let f(x) = be a piecewise function. Although f(-1) = 0 and f(1) = 1. f (r) +…

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Q: Given a set E c (0,1) of measure 0, construct a continuous non-decreasing function f : [0, 1] → R…

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Q: Let f(x)=4x^2-2x-2 find the following: 1) f(x+h)= 2) (f(x+h)-f(x))= 3) lim h→0 (f(x+h)−f(x))/h 4)…

A: We have to find 1) f(x+h)=2) (f(x+h)-f(x))=3) lim h→0 (f(x+h)−f(x))/h4) Find the equation of the…

Q: for a given function f (t)= f(-t).  what type of symmetry does f(t) have

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Q: Sketch the graph of a continuous function y = f(x) such that : a. g(2) = 2,0 2, and g'(x) →-1* as…

A: (a)  Find the behavior for g (x).

Q: If f is differentiable at xo, prove that f (xo + h) – f (xo – h) – f' (x0) - lim h-0 2h

A: Given that: f is differentiable at xo   To prove: limh→0f(x0+h)-f(x0-h)2h=f'(x0)

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Q: Let † : R² → R be the function x2 if (x, y) + (0,0) f (x, y) = x + Y if (x, y) (0,0) By using the…

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Q: Consider the piecewise-defined function S-x+ 2, if x < 2. f(x) = 1x-2,if x 23 %3D 7. Evaluate f(x)…

A: Given,            fx=-x+2,if x&lt;2x-2,if x≥3

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Q: Let F(x) = Vg(x). Find a formula for F'(x) in terms of g(x) and g'(x). Use your formula from (a) and…

A: Fx=gx Differentiating with respect to x, we get F/x=12gx·dgxdx    ∵dxdx=12x=12gx·g/x=g/x2gx

Q: If f(x) and g(x) are defined on domains A and B respectively, then the domain of f(x) + g(x) is? *

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Q: 4. Use the limit definition of the derivative to test whether the following function f(x), given by…

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Q: (i) Let ƒ be the function defined on (-o, 0) by f(x) = r$(3 – x)}. (2 – x) -2 Given that f'(x) = and…

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Q: If f is C2 on an interval prove that f(x + h) – 2f(x) + f(x – h) lim h-0 = f" (x). h2

A: We can prove this with the help of Lagrange Mean value Theorem as follows.

Q: ⎪ ⎨ ⎪ ⎧x^2 − 1 , − 1 ≤ x < 0 2x , 0 < x < 1 1 , x = 1 −2x + 4 , 1 < x < 2 0 , 2 < x < 3 a) Is f…

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Q: Show that the following statement is false by drawing a graph that provides a counterexample: If f…

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Q: If f is a function of only r, g is a function of only y, and f and g satisfy In(f(x)) + In(g(y)) =…

A: Given: f is a function of the only x and g is a function of the only y.…