Identify the invariant points of f(x)=4x+2 and it's inverse. Justify your solution.

Q: Find the second derivative of f(x)=(3x2+7)2 and simplify

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Q: The derivative of f(x) = 3 (22 + 4x) is - O 3x + 12 O -3x-2(2x + 4) 3x-2(2x + 4) O 3 -3x-3 (2x + 4)

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Q: Find the second derivative of the function.

A:

Q: Find the derivative of the function. f(x) = (2x³ – 8x?+ 7)1

A: topic - derivative of a function

Q: what is the inverse of the linear function   h (x) = x+7/4?

A: The given function is: h(x)=x+74

Q: -f(x) = x* – 6x³ –+ Vz7 %3D f'(x) = %3D id x5

A: Given,            f(x) =72x4 - 6x3 -2x5+x73

Q: The derivative of f(x) =3 4 is %3D

A: Consider the given function, fx=4x5 The property of derivative is defined as, ddxxn=nxn-1 Convert…

Q: Find the second derivative of the function.

A: From the given data:

Q: f (x) = 3 · 5" + e 4x²+7¤

A: We have to find derivative

Q: Find the second derivative of the function. f (x) = 5(2 – 7x)*

A: Find the second derivative of the function

Q: Find the second derivative of the function. f(x)= (3x³+6)* %D

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Q: what is the inverse of the linear function  f (x)2/3 x - 6?

A: Solution: Consider the given linear function is: f(x) = 23x - 6 A function g is the inverse of f if…

Q: Find the higher-order derivative. f"(x) = 16x³ – ? 34x f'"'(x) = %D

A: To find the third order derivative , we need to differentiate the gives function with respect to x.

Q: Find the first, second, and third derivatives of f(x) = x^4 − 2x^3 + 2x^2 − x + 8.

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Q: 4. h(x) = x+ 1

A: INVERSE FUNCTION If the input a of f  yield output b, then the inverse of the f yield a as output…

Q: Find the third derivative of the function f(x)=2x5-7x4+4x2-8x+11.

A: on doing diffrentiation with respect to x we will get

Q: Find the function that has an output of 16 when x=2, and has zeros 1 and −2i.

A:

Q: Solve f(x) > 0, where f(x) = (x – 1) (x + 3).

A: Function, f(x)>0, implies the value of the function lies to the right of the origin in cartesian…

Q: Apply the three-step method to compute f'(x) where f(x) = 9x² + 2. %3D

A: Given  f (x) = 9x2 + 2 .

Q: Find the second and third derivative of the function (a) f(x) = x6 – 3.x5 – 41x – 73 - |

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Q: Find the domain of the function.

A: Domain is set of all the input values which can take value in function such that it gives some…

Q: f (0), where f (x) = x2 + 2x + 2

A: Consider the given function: fx=x2+2x+2

Q: differentiate the expression with respect to x, assuming that y = f (x). (x2 + y2)3/2

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Q: Find the derivative of f(x)= 5x2 (4+5e")?

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Q: Linearize the function f(x) = x3 + 2x + 4 at a = 3.

A: To linearize a function  at certain point x=a , first we need to evaluate the function value at a (…

Q: Find the inverse 0f             y =f(x)= x2, if x ≥ 0. Graph f and f -1.

A: A function g is the inverse of function f if for y=fx,  x=gy Inverse of x2:y=x2Replace x and…

Q: Find the second derivative of the function. f(x) = 15x5/2

A: Consider the following formula: ddxxn=nxn-1 Consider the following function: fx=15x52 Differentiate…

Q: If (f(2x*)) = 6z°, calculate f'(x). f'(z) =||

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Q: Find the first and second derivatives of the function. f(x) = 11x1 + 6x - x %3D f"(x) = f"(x) =

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Q: Plot f (x) = x e - x and use the zoom feature to find two solutions of f (x) = 0.3.

A: Using a graphing calculator we plot f(x)

Q: Find the inverse of f(x) = x2 - 1 if x ≥ 0. Graph f and f -1 in the same rectangular coordinate…

A: Given: fx=y=x2-1 for finding inverse of given function, first we find x in terms of y then replace x…

Q: Differentiate the function (3x? – 4)2 f(x) %3D x2 + 1

A: Given: fx=3x2-42x2+1 To Find: To differentiate the given function.

Q: Let f(x)=4(13)2x. Which is equal to f(1)?

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Q: Solve the DE f'(x) = 5x given that f(0) = 3. %3D

A: The objective of the question is solve the  DE with help of given conditions.

Q: Evaluate f(x – 1)Vxª – 4x – 2dæ -

A: Given:      ∫x3-1x4-4x-23dx      =∫x3-1x4-4x-213dx   substitute u=x4-4x-2…

Q: Find the first and second derivatives of the function. f(x) =x4 -3x3 +16x

A: To find the first and second derivatives of the function. fx=x4-3x3+16x

Q: Solve the DE f'(x) = 5x given that f(0) = 3.

A:

Q: Integrate the function. dx x2 ', x > 8 Vx2 - 64

A: To integrate the given function

Q: Find the second derivative of the function.   f(x) = x2 + 7x − 4

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Q: Find the derivative of the function.

A: The given function is gx=3x2-22x+3-2.

Q: Find the second derivative of the function. h(x) = 6x−2 + 7x2

A: Given function is hx=6x-2+7x2   Differentiate the function with respect to x.…

Q: 3. At what point will the graph of f(x) = 2x – 5 and its inverse intersect?

A: 3. The given function is f(x)=2x-5 Note:   Multiple questions are given, we are answered with only…

Q: Find the derivative of the function. f(x) = x2 + 5 − 3x−2

A: Known fact: ddxxn=nxn-1ddxf±g=dfdx±dgdxddxk=0   where k is constant

Q: Find the Derivative of the Function: 2x2 3 | f (x) 5x? 6

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Q: Find the first and second derivatives of the given function. f(x) = 5x3 − 6x2 + 6

A: The given function is f(x) = 5x3 − 6x2 + 6. The derivative of xn is given by: ddxxn=nxn-1 and…

Q: What is the linear function of f(x)= -1/2x

A: Linear function

Q: What is the inverse of the function f(x) = 4x* – 1? %3D -

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Q: Identify the invariant points of f(x)=4x+2 and its inverse.  Justify your solution

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Q: Find the inverse of the function. f (x) = 5+ V3x – 3 -

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.