Let f:R → R be defined by: x - 1 x +1 if x s0 if x >0 f(x) : Then f]- 3,0[)= 1-2.oL

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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Q: Describe the x-values at which f is differentiable

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Q: Consider two functions, f: R2 → R and g: R² → R, such that. • fis C² 2 4.5 = [33] ● g is defined by…

A: f:ℝ2→ℝ and g: ℝ2→ℝ f is C2 Hf4,5=2-1-13 g is defined by gx,y=fx-y,yx

Q: For the function Sx² - x x² – if x 1 ’ evaluate the left and right limits as x → 1.

A: We can make it easier for you.

Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 => x = 0 and y = 0

Q: Determine and graph the domain set of the function f(x, y) = ln(x²+9y2-81) ==

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Q: |- Let f(x, y) = y²e* +y find fryy

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Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x°, f2(x) = x² + 1 [-1, 1] on…

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Q: x4 – 10 хе (-о, л — е) 2: х4 +9 хе [л— е, оо) - f(x) = Evaluate f(0)г

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Q: Determine the function of equation (u) a (1²5) ²= if a<B? a) 2) 1 32 2 4) It is impossible Leio to…

A: Given that,  f(x) = a (x-5)2 Here a &lt; 0  Clearly  f(x) = 0 a (x-5)5 = 0 Implies (x-5)2 = 0…

Q: Q2\A\ Which of the following functions are bijective 2- f: R{0}→ R\{0},f(x) = 1/x این 2- f:R→R,f(x)…

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Q: The function f(x) = 2 + 1/x is continuous on the following interval EXCEPT. O a. [-2,-1] O b. [1,2]…

A: At any point a for a function f(x) the limit limx→afx=L exists if the limx→a−fx=limx→a+fx=fa.

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: Determine L[f]if 0, f(1) = {1- 1, 0 2. 1,

A: Given that, A function f(t), t ≥ 0, its Laplace transform F(s) = L{f(t)} is defined as

Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

A: Answer

Q: Let f: A-XX Y be defined as f (a) = (f, (a). f2 (a)) each a A, Then f is continuous if and only if…

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Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

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Q: Let B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3) Show that the function g is surjective.…

A: We are given that B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3). We need to show that g is…

Q: Let f be the function defined by f (x) = x³ – x² – 6x. What is the absolute maximum value of f on…

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Q: Define f: R-&gt;R as follows: f(x)=x-[x] if [x] is even. f(x)=x-[x+1] if [x] is odd. Determine those…

A: To find the points where the given function is continuous.Take two cases:Case 1: Let x = a is an…

Q: Show that f(x) = e describes a bijective function from R to (0,+x). (a) Show that f is a function.…

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Q: f :R →R, f(x) = 3 + ax² + bx +11 fonksiyonu (-3,5) aralığında 20 - azalan ise atb-kaçtır ? If the…

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Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: a) f(x,y) = x³ + y³ + y(3x²y+ 3ry²) b) f(x,y) = x² + iy³

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Q: Suppose f: X→ Y, and A, B CY. Prove that (a) f¹(AUB) = f¹(A) U f¹(B).

A: Union of two sets A and B is denoted as A∪B  It contains all the elements that are either in A or in…

Q: et f(x) = |x| where xeR. Discuss the continuity and differentiability of f(x) at x = 0

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Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: show that f,given by f(x) x +0 )is continuous on R-{0}

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Q: O Find the largest value of A such that the function f(x) = x + 1x? - 4x + 6 is decreasing for all x…

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Q: Let f : D → E be a function and let A C D, BC E. Prove the following: (a) f(f-1(B)) C B. (b) If f is…

A: The function is f:D→Eand A⊆D and B⊆E

Q: The function f(x) = x² + 1 satisfies Rolle's Theorem in the interval [-2, –0.5]. - x² Select one: O…

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Q: ) Let f: R → R be defined by f(x) = 5x³ – 7x – 10. Prove that if |x| ≤ 3, then |ƒ(x)| ≤ 166.

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Q: uestion 6: Suppose f: N N has the rule f(n) = 3n²-1. Determine whether f is 1-1.

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Q: Let f(x, y) : = x/Y Evaluate f(3, 4)

A: We need to evaluate f(3,4) To evaluate we need to plug in 3 for x  and 4 for y

Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π