Find the inverse of the bijective functions below: a) f: R+ → R*, defined by f(x) = x² . %3| b) f: R+ → R+, defined by (x) = 2e3x-1 . х if x20 12х if x< 0 c) f:R → R , defined by f(x) =

Q: Show that the function f(x) = 2x³ – 1, from f: R → R is bijective and find its inverse.

A: The function f(x)=2x3-1, from f:ℝ→ℝ

Q: 6. Use an appropriate substitution to prove f(r)dr = f(a + b – x)dr. %3D

A: We have to prove definite integral property.

Q: Z→ Z be such that f(x) = 4x + 2. Is f invertible, and if so, find its inverse function.

A: Given query is to find the inverse function.

Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: Find a codomain B such that ƒ: A → B, ƒ(x) = e²´ is surjective. Show that g: B → A, g(x) = Vln x is…

A: As you asked only subpart (C) and (D) So, I answered here only subpart (C) and (D).

Q: Assume that f is an odd function defined on R and t e Rt. Compute

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Q: Find the linearization L(x) of f(x) at x = a. f («) — 4а? + 2а — 3, а — -5 -

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Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

A:

Q: Let f: [1,1]→ R be a function given by f(x)=2x-x2. Then the inverse image (preimage) of [0,4] under…

A: The answer is option D

Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: Let z = f(x, y) = 4x² + 2xy + By, Step 1 of 4: Evaluate f(3, 1).

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Q: Let f(x) = Vx. Compute the difference quotient for f at a = 7 with h = 4. %3D %3D

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Q: A function f: Z x Z is defined as f(m, n) = 3n - 4m.  Verify whether this function is injective and…

A: f: Z x Z is defined as f(m, n) = 3n - 4m So, f(m, n) = f(a, b) implies, 3n - 4m = 3b - 4a i.e. 3(n…

Q: u² -v² +uv x=In", y=' (11–v)-

A: two functions x=lnuv...........(i) and y=u2-v2+uv(u-v)2..........(ii) are given. To find the…

Q: Suppose f and g are differentiable functions on R such that,

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Q: Let F(x)= ^4sqrt(x) A. Find the linearization of F(x) at x=16 B. Use your answer in part (a) to…

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Q: Verify Mean value theorem in the following cases (a) f(x) = 2 x² – 10x + 29, on [2,7] (b) f (x) =…

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Q: Is the function f (x) below continuous on [3,+0)? (0, x > 0 X, 0 3 Choose

A: This question is related to limit and continuity, we will solve it using given information.

Q: Show that the function f : R−{−2} → R−{1} defined by f(x)=x+1 / x+2 is a bijection, and find the…

A: Topic = Functions

Q: Glven that f() = 6x + 2 and g(x) = 1 - x, calculate

A: Given, f(x)=6x+2g(x)=1-x2f[g(x)]=f(1-x2)          =6(1-x2)+2          =6-6x2+2          =8-6x2Hence,…

Q: Find a function f(x), such that f"(x) = 3sin(4x). %3D

A:

Q: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

Q: Consider f : R+ → [4, ∞) given by      f(x) = x2+ 4. Show that f is invertible with the inverse f-1…

A: The given function is

Q: Suppose f(x) = 4nx?e-Tx -e-n for all x € R. Show that f = -f. %3D

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Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

Q: Show that f (a) = is Libschitz function on r+ 2

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Q: Determine the antiderivative F of "f" , which is defined by f (x) = 4x3 – 6, where F (0) = 3 %3D

A: Consider the given function fx=4x3-6

Q: The domain of f(x) = /1 – I In(x) is %3D

A: The domain is the set of all possible x-values which will make the function give real y-values as…

Q: Use f (x) = -2 In(x + 1) to do the following: %3D

A:

Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

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Q: Let f be a function defined by: f(x) = ln(22x). In Then, f-¹(x) = e¯* + 2. ос إختر واحداً: True…

A: Topic = Functions TRUE

Q: ) The domain of the function y = In(1 – x²) is R – [-1,1].

A: Log (x) is defined for every  x is positive real number .

Q: Algebraically show that each of the given combinations are equivalent to the given functions. If…

A: This question can be solved using the concept of multiplication of two algebraic function.

Q: Use this definition to find f'(a) at the given number a. f(x) = V6x + 7,

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Q: Find the inverse function of the function f(x)= 2x on the domain r of (2) = () Of (z) = %3D Of (2) =…

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Q: Given that y(a) = f(9(x)) and g(3) = 1, gʻ (3) = 2, f'(1) = 2, compute y' (3). x° + 2x Let f(x) x3…

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Q: 13) Evaluate div F where [[x, 4₁27 = <-xy, x², 2³ e xy² ) 32 *** - ) 2xyz e ) 242 243 - ۶۶ ) *+3x 3…

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Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

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Q: Consider the functions g : R→ R defined by g(x) = x^2+4, x∈R and h : R→R defined by h(x)=x−2 ,x∈R.…

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Q: Use this definition to find f'(a) at the given number a. f(x) %3D 6х°, а %3D -1

A: Consider the given function. fx=6x5 The objective of the problem is to find the value of f'(a)  at…

Q: Show that the function f:R to R defined by f(x)=5x-12 is continuous using the E-d definition

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Q: Use FTC I to prove that if |f '(x)| ≤ K for x ∈ [a, b], then |f (x) − f (a)| ≤ K|x − a| for x ∈ [a,…

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Q: Let f : N → Y be a function defined as f(x) = 4x + 3, where,                                 Y = {y…

A: Given:

Q: Let f' : N → R be a function defined as f'(x) = 4x2+ 12x + 15. Show thatf : N→ S, where, S is the…

A:

Q: Let f : 0, 1] R be defined by f(x) = {1+a, a € Q .2 Then Jo f is

A: Given: f:0,1→ℝ defined by fx=1+x, x∈ℚx+x2, x∉ℚ To find: ∫01f=? Used formulas, ∫xdx=xn+1n+1∫dx=x

Q: Prove that the function f : R → R given by f(x) = 3x° – 2x is continuous at 1 using the a.…

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Q: Consider the function f defined by the formula ( ax2 + bx – 3b if x 1. Determine the values of a…

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