Let f be the function defined as follows: [3-x, for x <1 f(x)= {ax + bx, 5x-10, for 1

Q: Let f (x) be a function satisfyingIf (x)| <x? for -1<x< 1. Show that f is differentiable at x = 0…

A: The solution is in step 2

Q: Use the definition of 1 1 to prove that the given function is 1 - 1. Let f:R → Rwith f(x) 3(x - 4)

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Q: compute f(x)-f(a)/x-a for the following function f(x)=x^2-3x+1

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Q: f is a function of all real numbers defined by f(x)=x2, what is f-1({x |0<x<1})?

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Q: Let F be function such that F(1)=7 and F' (1)= −5. Find H′(1) for the function h(x)=f(x)f(x).…

A: Using differentiation ,

Q: Suppose f is a function which satisfies the properties: f(x + y) = f(x) + f(y) + x²y + xy? for all…

A: Given that, f(x+y)=f(x)+f(y)+x2y+xy2 for all real numbers 'x' and 'y'  and, limx→0f(x)x=1   As we…

Q: Let f(x)= {x^2-6+12, if x≤-1/ax+b if x>-1 Find a and b such that the function f(x) is…

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Q: For what value of x is the function f(x)=4/ x2-x-12 not continuous

A: Topic-continuity

Q: Let f and g be the functions defined by f : R → R+ ∪ {0} with f (x) = x2 and g : R+ ∪ {0} → R with…

A: (fog)(x) is the value of the function f(x) at g(x) (fog)(x)= f(g(x))

Q: Let f(x) be defined by Find f'(1). f(x) = (2x - 1).

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Q: Check the continuity of the functions f given below at 1 and 2. x +1 if x < 1 f(x) = { 2x 1+ x'if x…

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Q: let f be the function x²-C for x< 5 flx)=3x+5c for X Z 5

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Q: For the function f defined by f(x) = x2 - 4x + 1,

A: Given function: fx=x2-4x+1

Q: Suppose f is a function which satisfies the properties: f(x + y) = f(x) + f(y) + x²y+ xy? %3D for…

A: Given that: fx+y=fx+fy+x2y+xy2limx→0fxx=1   Concept used: Derivative of fx is given by…

Q: Check the continuity of the functions f given below at 1 and 2. x +1 if x < 1 f(x) = 2x if 1<x<2 %3D…

A: By definition of continuity at x=a :- L.H.L = R.H.L = f(a)

Q: Define functions f and g from R to R by the fol- lowing formulas: For every x E R, 2x° + 2x = 2x and…

A: It is given that, f(x) and g(x) are defined from R to R by the following formulas:

Q: . Suppose that f(r) is a function given by for 0<r<7, f(z) = for -n <I<0.

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Q: Let f be a function such that -² ≤ f(x) ≤ x² for all x ER. Show that f is differentiable at x = 0…

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Q: Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1+ (F(x))*. What is…

A: Given that f(g(x)). = x  and f'(x)= 1+(f(x))2 and we find g'(x). Here i attached solution of this…

Q: (b) Suppose f'(x) > 1 for all x > 0, and f(0) = 0. Show that f(x) > x for all x> 0.

A: We will be using mean value theorem

Q: x²-4 f(x)%3D x2-5x+6

A: As we know that; The polynomial function y=fxgx is continuous everywhere except such ''x'' where…

Q: Given the following function f, define f(5) so that f is continuous at x = 5. x2 - 10x + 25 f(x) =…

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Q: Let f be the function defined above, where b is a constant. For what values of b, if any, is f…

A: Left limit at 3 should be equal to right limit at 3 for the function to be continuous.

Q: Let f(x) = Vx +7 and g(x) = x +3 a) Find (2) (2) show work. b) Give the domain of the function (-)…

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Q: True or false: For the function f(x) =1/(x - 3), f is not defined at 3, so f is discontinuous at…

A: True or false: For the function f(x) =1x-3, f is not defined at 3, so f is discontinuous at 3.

Q: Let f be defined as follows: x 0

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Q: Let f(x)=x^3−9x. Using Rolle's Theorem, what are all the values c in the interval [-3, 3] such that…

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Q: Let f be a piecewise-defined function given by the following. Determine the values of m and b that…

A: Topic = Derivative

Q: Consider the function defined by (x² (6x – 9 if x 2 3 if x < 3 f(x) = {-9 a. undefined b.…

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Q: x +1 if x 2 if 1<x<2

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Q: let F be the function from R to R defined by: f(x) =x². Find f–¹({1})

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Q: show that any function f(x) defined on a symmetrically placed interval can be written as the sum of…

A: Here we have given one function, and we have to prove that the function f(x) can be written as the…

Q: Explain if the function is continuous or not for the given number a. if x>1 if x = 1 ,a=1 if x<1…

A: we have given function     we need to determine the continuity at a=1

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: assume f(g(x))=x and f'(x)=1+f2(x) for all x. show that g'(x)=1/(1+x2)

A: Differentiate both sides of f(g(x))=x with respect to x. Use chain rule on the left side.

Q: Let f(x) be the function x + 5 for x 2.

A: Let f(x)=x+5 for x&lt;-1               =cx for -1≤x≤2                =x+6 for x&gt;2 To find the…

Q: а. Determine the discontinuities of the following functions and state why the function fails to be…

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Q: Let f be the function defined by f (x) = 6x. On which open intervals is ƒ decreasing? %3D -2 3 <글…

A: Given that: f(x)=x33-x22-6x

Q: Hello, I need help solving the following. It is known as an "initial value problem."

A:

Q: Let f(x) be defined as Find f'(1). f(x) = x² + 2x - 3 2 x + 1

A: Given that a function f(x) and we find f'(1) or derivatives of f(x) with respect to x and then we…

Q: Let f(x)= {x^2-8x+16, if x≤3/ax+b if x>3 Find a and b such that the function f(x) is differentiable…

A: Given fx=x2-8x+16x≤3ax+bx&gt;3 is differentiable everywhere so it is also continuous.

Q: If f(x) and g(x) are defined on domains A and B respectively, then the domain of f(x) + g(x) is? *

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Q: If f(x) is a function that is defined for all x E R, then f(ƒ-'(x)) = = x. True

A: Let,  f(x) = a*x+b f-1(x) = (x-b)/a

Q: For the shown function, find A so that the function is continuous at 1.

A: Consider the function: f(x)=x2          if x&lt;1Ax-3 if x≥1 . Theorem- The function is continuous…

Q: a. f(x) x-2 x-7 b.f(x) = r2+1

A: (a) the given function is f(x)=1x-2 the function is continuous in interval [a,b] if it is continuous…

Q: Given that f(x) = 5x – 13 where f(x) = y, define a function rule for f-1.

A: Given function, fx=5x-13 The objective is to find the inverse function. y=fx⇒f-1y=x The following…

Q: Show that if f is symmetric with respect to x = a, then g(x) = f (x + a) is even.

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Q: 2. Let f be the function defined by 9) f (x) = x²+2x+1 ,Find: -f (3) +fヒ3)

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Q: Determine what, if any, value to assign to f(a) to make f continuous at x2-5x+6 f(x) = %3D ;a= 3 x-…

A: We have to find the value

Q: Let f(x) = 2x² + 5x - 7 x-1 = 1 and determine what value for f(1) would make Show that f(x) has a…

A: Solution of given question is written in below steps.