1. Let int r + 2 f(x) = int x – 2 where int r is the greatest integer function. (a) Find the domain of f. (b) Is ƒ injective? 2. If two functions f and g have inverses, then (f og)-1 = g-1 of-!. Let f(r) = 2x – 1 and g(x) = 3x + 4. Find the following: (a) f-'(x) (b) g-'(x) (c) (f o g)-'(x) (d) (go f)-'(x) (e) (f-1 og¬1) (x) 3. Does every odd function have an inverse? Give a counterexample. (A counterexample is an example that disproves a statement. For example, to disprove the statement “every whole number is even", a counterexample would be 3.) 4. Find a quadratic function of the form f(x) = ax² + bx + c that satisfies the following conditions. The graph of f passes through the point (1,5) and has vertex (-3, –2).

Q: -бх +3х?-2х +1 y =

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Q: 11. (a) State the largest possible domain of the following functions: opk fix → x-3 x+2 h:xx²+3…

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Q: Explain the Wronskian of 2 functions f and g ?

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Q: What is the domain of the secant function?

A: Secant function , Sec xWe know        Sec x=1cos xTo find domain Put cos x=0

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Q: If f(z) <0 for all real numbers z then f is decreasing on (-o, 00) Select one: O a. False O b. True

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Q: How do you show the inverse image of the intersecction of S and T equals the intersection of the…

A: To prove : f-1(S∩T)=f-1(S)∩f-1(T) To show f-1(S∩T)=f-1(S)∩f-1(T) need to prove…

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Q: '(x) = ( 13 + x1, (x-1)², x x

A: T(x)=|3+x|x&lt;-1(x-1)2x≥-1

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Find the absolute extrema of the following function on the indicated interval.  f(x)=x^3+2x^2-3x+4…

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Q: (f) Evaluate f(-1) and f(1). Can you conclude that there is no zero on the interval (-1, 1)? Explain…

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Q: 3) f = {(0, a), (1, d), (5, e), (9, c)} find the inverse of this function.

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Q: Let X=[-1,1] and Y=[0,1], and define the function f:X-->Y by f(x)=x^2. Which of the following is NOT…

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Q: Based on the definition of divided difference, show that f[x1,x2,x3] = f[x2,x1,x3

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Q: Consider the possible functions from [7] to [9].  How many in which f-1 is not a functio

A: Let f:7→9 is a function then, Let A=[7] and B=[9] So, n(A)=7 and n(B)=9 Now, the total functions of…

Q: 1 Compute and simplify the difference quotient for f(x) = V1- x

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A: Given- fx=cosh-1x8 To Find- The domain of the function.

Q: J 3(x)is even function 0 صواب ihi O

A: We will use the fact that j_-n(x) =(-1)^n j_n(x) to decide whether j_3(x) is even or odd function.

Q: How do you show the image of the union of S and T is equal to the union of the image of S and the…

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Q: 53. H(z) = sec“(/=)

A: Topic : Function

Q: 1.) fex) =x3 -x²+4x +2 2.) FCxS= -x3+ Sx-2 %3D

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Q: Differentiate the function.

A: Given function -f(u) = lnu1+ln(2u)Differentiating with respect to u - f'(u) = ddulnu1+ln2uf'(u) =…