Find f(2021) if the function f satisfies following conditions: f(1)=1 f(x+y) = f(x) + f(y) for all x,y element of R f(1/x) = f(x)/x2 , x!=0

Q: Prove algebraic ally that any function of the form f(x)=ax2n+4 (where n is an integer) is symmetric…

A: The given function is fx=ax2x+4. To prove fx=ax2x+4 is symmetric to the y-axis, it is enough to…

Q: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: Find the maximum point for the function f(x) = 1 + 12x – 4x O (-1, -7) O (2, -7) O (0, 1) (1, 9)

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Q: 1 g(x) = /3 — х

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Q: of and ду of For the function f(x,y) = In (x+ 3y), find

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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: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: Find x-intercepts of the function: x2 – 9 f (x) = Зх + 1 Select one: O a.x = 3 O b.x= -3, x= 3 C. X=…

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Q: Let f(x) = 1+ V7x +1. Determine the largest possible domain of f(x) Select one: • [-1/7, +o0)

A: Given function is  fx=1+7x+1

Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval [0, 4]

A: Use critical value and end points for absolute maxima and absolute minima.

Q: Which of the following functions passes through the point(0, 10) and satisfiesf'(x)= 87

A: given f'(x)=8

Q: In(2 - a) x² + y² – 16' Determine the domain of the function f(x, y)

A: The domain of a function is the values of the variables of the function that result in a defined…

Q: - Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that…

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Q: z) = (x2 + then (a + E

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Q: Let f be the function defined by ƒ (x) = x² − 12x³ + 48x² − 64x. Which interval is the graph of f…

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Q: Fxy(x, y) is a monotonic and non-decreasing function of both x and y.

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Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

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Q: Define f(x ) = Vx2 +1 and g(x) = 2 – x2. State the domain of (f + g)(x ). x # v2, –v2 - [-1, 00)…

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Q: Determine the type of functions from R to R with necessary figure. i) f(x) = 5x + 7 ii) f(x) = (x² +…

A: (i) fx=5x+7 This function is state line and has roots is x=-75

Q: Q1 a) let f be a function defined as f(x)=3x² + 2x². Find f(2), f(-1), f(1). b) Define functions f…

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Q: f (x) = x 2 satisfies the Horizontal Line Test on the domain {x : x > O}.

A: Horizontal line test is a test used to find the function is injective that is one-to-one. First…

Q: Select the following functions that are bijective. ƒ₂: R → R, ƒ₂(x) = 14 f₂: R → R, f₂(x) = x f₁: R…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.