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: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

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Q: Let f(x)=xsinx+V1-x Evaluate f'(-). Select one: а. 2 b. 0 C. d. 3

A: According to product rule of differentiation and according to power rule of differentiation .

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that…

Q: Suppose f is differentiable on the set of real numbers R and a E R. Let F(x)= f(xª) and G(x) =…

A: F(x)=f(xα)F'(x)=f'(xα)ddx(xα) , [chain…

Q: Let R={(x,y) ERxR: |x| = |v|). Then R a function on R. оо True False

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Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

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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: 3. Find the domain of the following functions: a.) f(x) = V1-x Inx b.) f(x) = Vx - 1lr

A: solutionsince the given (3)(c)f(x)=1-xlnx(b) f(x)=x-l ln(x)use have to find the domain of the…

Q: 5. Prove that the function f: Z → Z defined by f(x) = 3x + 1 is one-to-one.

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Q: Identify and sketch the domain of f(x, y) = 4x² In x Y

A: For function to be valid denominator must be non zero and log has non-negative real numbers and…

Q: Let f : R → R be a function defined by f(x) = Decide whether it is an injection, a surjection, 1+ x2…

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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: lim 3i 4 +

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Q: The absolute Extrema of the function f(T) = -x-* -21/3 +r on the interval [ 8, 1] are Select one: a.…

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Q: How many functions f:R→R  exists such that : 2f(x)+2f(y)=f(x+y)+f(x−y)+2y holds for all real x and…

A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: Suppose f: R → R is a function defined by f(x) = x³. (a) Find f([-1,1]) and f-¹([0, 8]). (b) Show…

A: We shall use the intermediate value theorem to answer this question

Q: if f (r) is differentiable prove that f(r)r is irrotational

A: The objective here is to prove that the vector field f(r)r is irrotational. Given: f(r) is…

Q: (c) Evaluate the Riemann integral ₁¹(x) dx by using definition with the parti- tion 2n=1,2}, n+1 =…

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Q: Let f(x) = x. Show directly that f ∊ R[0, 2]

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Q: Let f(x, y) = Evaluate f(5,5) 175 - 3x² - 4y2

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Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…

Q: Let f : R → R be defined as                   f(x) = 10x + 7. Find the function            g : R → R…

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Q: 4. Show that the function f: R → R defined by f(x) = x² - 3x + 1 is not one-to-one.

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Q: f : R --> R is defined by f(x) = 2x+1, A= (0,1)  and B = [ -1,1 ]    find f [A] and f-1[B]

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Q: Show that the function f : R → R given by f(x) = x3 is injective.

A: To show the given function is injective(one-one), first calculate the value of function at two…

Q: Show that the function f : R → R given by f(x) = x/(1+|x|) is increasing.

A: To find when a function is increasing, you must first take the derivative, then set it equal to 0,…

Q: Form the PDE by eliminating the arbitrary functions from the relation z = f(xy)

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Q: Let f(x,y,z,w)=45x3z-1/y+wz3. Evaluate f(a,b,c,d) where a,b,c are non-zerol real numbers

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