Show that f:Z-->Z ; f(x)=x+2 is invertible

Q: Show that f (x) = 1 is not uni form continuous on (0,3) I-3

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Prove that f(x)= 2x-tan^1x-ln(x+√x^2+1) increasing on [0, infinity]

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Q: The graph of f(x)= - x2-1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 ).co (-∞, – 1)U…

A: Given, fx = xx2-1  We have to find the interval in which graph of  fx = xx2-1 is concave up.

Q: branch of z1/5 that is not continuous and positive on the imaginary axis?

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Q: Show that F = ху, , zy) is not conservative. 2

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Q: Show that the function is continuous. (x) = 3x cos 3x

A: Show that the function is continuous. (x) = 3x cos 3x

Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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Q: The best approximation of f (x) = cos(3 + x) by a %3D Fourier polynomial of degree 1 is 1) F(x) =…

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Q: Find the absolute max and min of the function F(x)= 2sin(x)-cos2(x) on the interval [-π, π]

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Q: Prove that f(x) = [[sin²(2log r)– 3 sin ( 2logt)+2] dt %D 1. Cannot be decreasing any where,

A: To prove that f(x) can not be decreasing anywhere, where f(x) is defined as…

Q: How can you apply the chain rule in calculus 3 with multivariable calculus

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Q: The inner-product function satisfies : Select one: a. = b. = 0 C. is greater then zero d. =

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Q: Use the definition of the hyperbolic functions to prove that 2cosh (x)-1=cosh(2x).

A: As per the instruction, we will be answering only the first question. For (a),      2 cosh2(x)-1=2…

Q: Let f: [2,3] → {1,3} be a continuous function such that the equation f(x) - x = 0 has a solution in…

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Q: (d) Is f invertible? If so, what is f-?

A: f:ℝ→ℝ is defined as  fx=x1+x⇒fx=x1-x, x<0x1+x, x≥0 f is both 1-1 and onto. Hence, f is…

Q: Find the interpolating polynomial for the function f(x) = e through the points x = 0, 1, 2.…

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Q: Prove that f(x) =- 2x(sinx+ tanx), is an odd function, where [] denotes %3D X+ 2n -3 the greatest…

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Q: find second derivative  number 5

A: Given: -

Q: Use Taylor's polynomial of degree 2 of the function f(x) = tan 1(x+1) + x² %3D about c = - 1 to…

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Q: Let f(x) =esin 3x + 2x a. find the linearization of f(x)=esin3x+2x at x=0. b. Use your linearizato…

A: a). Given f(x) =esin 3x + 2x f(x) ≈ L(x) = f(a)+f′(a)(x−a). where the function L(x) is called the…

Q: Calculate facterial funchion n -X x e %3D

A: Using integration by parts solve the integral:  ∫0∞xne-xdx=∫xne-xdx0∞…

Q: Is the scalar valued function f(x)=(x^2-1)/(x+1) continuous?

A: This is a problem related to limit and continuity of the function. Please follow the procedure given…

Q: Use moment generating functions to show that if X3 = X1 + X2, with X1 X3 - X V3 > vı, and X1 and X2…

A: Solution

Q: Determine all the critical numbers of f(x) = sinxcosx.

A: Determine all the critical numbers of   f(x) = sin(x)cos(x)

Q: what is the antiderivative F(x) of f(X) = 3x1/2-x-1 that satisfies the condition  F(4)= 0? A,…

A: The given function is fx=3x12-x-1 that satisfies the condition F4=0. Find the antiderivative of Fx.

Q: Show that the nth Maclaurin polynomial of f (x) = arcsin x for n odd is 1.3 x Tn (x) = x+ 23…

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Q: Let 'f be a continuously differentiable real valued function defined bx+a x<1 by f(x) = 5x² Then the…

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Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: Let f (æ) = + and 9(x) = 3 – ya. - 1 and g(x) = 3 – Vx. %3D Find the domain of (gof)(x). (0, 0) (-0,…

A: Now,

Q: b) Show that the function f(x) = x7 +1 is invertible %3D

A: Given that  f(x)=x^7+1

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: Show that the function f(x) = x’ + 1 is invertible from R to R.

A: First prove that the  function is one -one  let f(x)=fyx7+1=y7+1x7=y7x=y therefore, the function is…

Q: Use the Second Fundamental Theorem of Calculus to find F '(x) F(x) |Vt4 + 1 dt -7

A: 2nd Fundamental Theorem : For F(x)=∫axf(t) dt, if f is continues on [a, x], then F'(x)=f(x).

Q: Find the maximum value of f(x)=2sin(x)cos(x).

A: Given: f(x)=2sinxcosx The above function can be written as: f(x)=sin2x…

Q: Show that f (x) =++1 1 - is not uni form continuous on (-1,0)

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the g'(x) if: g(x) = 1 +t² dt 3x2

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Q: If f is continous on [0,1) ,then f has absolute minimum on(0,1) True or false?

A: Extreme value theorem says that, if a function is continous on a closed interval [b, a] , then it…

Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal…

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Q: Decide whether or not the real function In (cos 2x) 2x2 x + 0, f(x) = -1, = 0, x = is continuous at…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Use the Intermediate Value Theorem to prove that the equation e* = 4 - x³is solvable on the…

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Q: 7. Verify the validity of the Mean Value theorem of Lagrange in the case of f(x) = 2x3 – x +1 in the…

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Q: Suppose that the function f: R → Ris continuous and that its image f (R) is bounded. Prove that…

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Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

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Q: Find domain and range of the funetion f(x, y) In[e-x' -y'1

A: The ln function is undefined for negative arguments. This will ensure that argument is positive. So…

Q: Prove that it is impossible to maximiz

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Q: If f(x)=sin-'x. Show that (1-x2) fx(x)-xf (x)=0. HENCE ,prove that f^(n+2)(0)=n²f^n(0)

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Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…