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: Let f(x) f-¹(x) = 1 x + 11

A: we need to find the inverse of the function.

Q: Let f(x, y) = 125-3x²-2y2² Evaluate f(0, 3)

A: f(x,y)=sqrt(125-3x2-2y2)Find f(0,3)

Q: Let k(x) = 1 -x4, where j(x) = y + k(x) and y = x6 - x2. Describe the graph of j(x) based on the…

A: Given: k(x)=1-x4 where, j(x)=y+ k(x) y=x6-x2 Then j(x)=x6-x2+1-x4j(x)=x6-x4-x2+1 The zeroes of the…

Q: Let f(x)= x + 19 X - 16 Then f-1(x) = %3D

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Q: f (x) + 5 f(x) – 3 g(x) (4) Let f(x) = mx+b, where m and b are constants and m 6= 0. Prove that the…

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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: determine the value of the parameter a that will make the function f(x) = [ax+1, x- -1

A: The given function is fx=ax+1,    x<-1x2-3,     x>-1 To find: Value of parameter a

Q: The graph of function f(x) = x³ – 6x² + 9x + 1 is - concave upward on O (-∞0, 2) O (-∞, ∞0) O (2,…

A: The given function is: f(x)=x3-6x2+9x+1

Q: What are the valuesbof x where tge functions f(x) = (3x+2)(x+1)\x+3 is undefined?

A: Consider the function f(x)=(3x+2)(x+1)x+3

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

A: given f'(x)=8

Q: Find the domain of f

A: We have to find the domain of the function: fx=x+2+2-x We know for any square root function y=fx it…

Q: Solve the following differential equations (a) y/ = (b) = %3D ytev

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Q: Q: Let f: R→R be given by f(x)= x +3 Find (a){x: f(x)= 28} (b) The pre-image of 39 and 2 under f.

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Q: If f(x) = x + 9 – x and g(u) = u + V9 – u, is it true that f= g? Yes No

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Q: ,x2

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Q: Let f(x) ƒ-¹(x) = = 1 x + 13

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Q: Find a function f(1) such that | f(z)dr= 2² – 5.

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

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Q: Show that the function f(x)=√x+1 is differentiable in 2 = 2 but not differentiable in x = −1.

A: Given data:- The given function is, fx=x+1

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: Consider the quadratic function V(x)= ax +bx + cx +2x,x, -4x,x, -2x,x,, try to find the range of…

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Q: (x) = 2x - 3           x = 5 Compute f -1 (x

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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.