1. Let f(x)= (x– 2)3. Domain fex) i(-o, a) Range fx) : (-0, 0) (a) Determine if there are any restrictions on the domain of f for its inverse to exist. Damainf-():(-0, Range : (-no, a) (b) Draw f and f-l on the same coordinate axes.

Q: Ax, y) = In(x +y)

A: In this question, we have to find the domain and range of f(x,y)=lnx+y As we know that the domain of…

Q: 22. The function f(x) = Vx – 6 is transformed according to (x, y) → (7x – 7, - y+1). the transformed…

A: Substitute fx for y in the transformation and simplify. x,y=x,f(x)→7x-7,-f(x)+1=7x-7,-x-6+1

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 3x² + 2x – 5 at x = 0 %3D %3D…

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Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

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Q: Show analytically that the function f is not differentiable at x = x² x1

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Q: Determine the limit of f(x) as x approaches 2. * 51 f(x) 4- 5 4 2 -i 0 i 2 3 4 5 1- -2 3 5+ 3 1 DNE…

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Q: The definition of the first derivative of a function f(x) is: Select one: f(x+Ax)-f(x) a. f'(x) =…

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Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: if f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable at (2,F(2))   true…

A: Given statement is If f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable…

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

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Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: The function f(x)=(2-x)/(3) is continuous at

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Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: Show that f is not differentiable at x = 1 and has a corner in its graph there. x 1

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Q: 5. Use the Intermediate Value Theorem to show that the function f(x) = x³ + x² – 1 has a zero…

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Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

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Q: ,for x 1 Discuss the contuniuty of f andf'.

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Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

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Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

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Q: Determine all critical points for the function. f(x) = x - 12x - 1 3. %3D

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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: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: froblem 2/ Drive the function below. t-y=Vx-secx+3 2-y=(Secx + tanx)(secx – tanx) 4-4=5+ Cota tan 9…

A: we have to find the derivative of the following.

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: Let g be a function that is defined for all x, x 2, such that g(3) = 4 and the derivative of g is x²…

A: The interval where second derivative of function is positive, is the interval where the function is…

Q: Show analytically that the function f is not differentiable at x = 0. Ax) = 2x+1 x>1

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Q: 3 Show that the function f(x) = Vx – 5 is one to one function. %3D

A: The objectives to show that the function f(x) is one to one function.

Q: and g:y → X. If gof -Ix => Show that f is one-to-one function %3D and 8 is surjective function ?

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Q: 17 The function f is defined by f(x) = 5x - c, where c is a constant. In the xy-plane, the graph of…

A: Solve both the problem in the following way:- (i) given point will satisfy the function. (ii)…

Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

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Q: Discuss the continuity of the function g(x) = 1/(x^2-4) on the interval (0, 2] and [−1, 3].

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Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

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Q: 5. Determine the critical points of the function: f (x) In(x² + 4x + 14) %3D Enter your answer

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Q: 1 - X 0 3

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Q: 46. Let f(x) = x³ - 4x² . Find the points on the graph of f where the tangent %3D line is…

A: 46. The given function is fx=x3-4x2. Differentiate fx with respect to x. f'x=ddxx3-4x2=3x2-8x Now,…

Q: 6. Prove that the function f defined by f (x)= ,xe(-00,1), has an inverse function 1-x defined on…

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Q: Let f(x)=1x−2 ; for what values of x , f(x) will be discontinuous?

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Q: Let P=(x,y) be a point on the graph of y=square root of x a) Express the distanced d from P to the…

A: Please refer to the image below.

Q: C. Show that f(x) = (x26)² has no inverse on the interval (-∞,0).

A: Since you posted two questions here, i can answer only 1. Please reupload second question again.…

Q: 9. Discuss the continuity of the function x 2 x2,

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Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: 1) Find the absolute maximum and minimum for function f(x,y)=x²-xy+y²-6y-4, on the domain -4≤x≤2,…

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Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…

Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

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Q: Suppose that f is a function with f(2) &gt; 0 and f1(2) = 0. If f is a local minimum of f, what do…

A: It is supposed that f is a function with