1) f (f-1(x) 2) f-1(f(x) are equal to the identity function Find the inverse function of f (x)= 1/5x, Verify that both 3) f(f-1(x) 4) f-1(f(x) are equal to the identity function

Q: 5. Determine which inverse trigonometric function g has the derivative g'(x) = x* +1

A: We find the integration of g'(x) For that use substitution x=tanz

Q: Find the fifth derivative of  f ( x) = 3 x 3 - 7 x 2 + 6. Use correct notation.      f '''''(x) =…

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Q: x²-x+1 Find the derivative of the function f(x)=- o (2x)-(x²-x+1)xr-1/2 3/2+. 1/2-x-3/2 O…

A:

Q: Find a rule for the derivative of the product of four functions f,g,h, and k. Use your result from…

A:

Q: (a) Find the equation of the tangent line to the graph of the function f(x) = 3x² at the point (-2,…

A: (a)   Differentiate the function with respect to x is,   Substitute -2 for x in the above equation.

Q: Prove that the function f(x) = x 5 + 2x 3 + 4x − 12 cannot have two real roots. (Hint: Use the first…

A:

Q: Which statement is true? There are many anti-derivatives, f(x), of a function g(x). There is only…

A: Given

Q: -x² +1 Let f(x) be defined as f(x)={* - | 1–sin² x if x20 if x<0

A:

Q: Discuss the continuity of the composite function h(x) = f(g(x)).

A:

Q: The range of F (x) = 3 sin 2 x is -3≤F(x)≤3 -1≤F(x)≤1 -2≤F(x)≤2

A: The given function is: F(x)=3 sin(2x)

Q: Sketch a graph of the function f(x) = – 3 sin(3x). 4+ -5/6 -2/3 -/2 2t/3 5/6 -1 -2 3.

A: Topic = Graph

Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A:

Q: True or False, an even function is never invertible.  I'm having trouble understanding this

A: From the given information it is needed to prove whether even function is invertible or not.A…

Q: Verify that f′(x) = g′(x) and explain the relationship between f and g.

A: We have given fx=sin x-3xx, gx=sin x+2xx We have to verify f'x=g'x Quotient rule:…

Q: Example 0-12: What is the derivative of f(x) = 4x(x² + 1)3?

A: given

Q: Find f(x) if f "(x) = x -cos x, f ' (0) = 2 and f(0) = -2.

A: To find f'(x) from f"(x), we will integrate f"(x) c=integrating constant Given f'(0)=2 , using that…

Q: Differentiate the function. f(x) − x - 3 sin x

A: we have to differentiate the given function f(x) =− x - 3 sin x

Q: f(x) = -x/x-1, show that ½[f(x) + f(-x)] = f(x2)

A: The given function is fx=-xx-1.

Q: 2) Let f be a function given by (3x +2 if f(x) = { 3 (x² + 1_ if Find f(0), f(-2), ƒ(-1), ƒ(1) and…

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Q: Suppose f is a function with range (-∞, ∞) and g is a function with domain (0, ¤). Is it possible…

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Q: Suppose f is an invertible function and f^-1 is its inverse. Explain how we can use the chain rule…

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Q: Find a formula for the inverse function f' and verify that 50 (fof *)(x)=(f*of)(x)=x, if f(x)=; Also…

A: Given that  f(x)=501+1.1-x--- (1) To find f-1(x) Replace f(x) as y in (1) y=501+1.1-x Swapping the…

Q: Use Taylor's polynomial of degree 2 of the function f(x) = tan 1(x+1) + x² %3D about c = - 1 to…

A:

Q: If f(x) and g(x) are two functions defined on an interval then, ꭍ{f(x)±g(x)} is equal to?

A: The sum rule states that the integration of the sum of two functions equals the sum of the integrals…

Q: Find the inverse of the function on the given domain. (Enter the domain using interval notation.)…

A:

Q: Show also that the function ln(z) is unique up to addition of a constant 2πik, k ∈ Z.

A: ln(mn) =ln(m) +ln(n)  ln(am) =mln(a)

Q: 74. (-300, 0) 400 f(x) 210 1-10² (100, 0) 100 200 −1-10³) (0, –90,000) -2-10 -200 -100 3-10³.

A: For any polynomial equation from graphics can be given by as:  F(x)  = a(x-b)  (x-c)  (x-d)  Where…

Q: Find the derivative of f(x) = 8 In (2). Enclose arguments of functions, numerators, and denominators…

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Q: Find the domain of the function. f(x) = (6cosx)/(1 - sinx)

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Q: Let f(x)= x2 + sin x - 2 cos 2x. Find (f-1)'(-2)

A: Given: fx=x2+sinx-2cos2x To find: f-1'-2 Now, we know that f-1x' = 1f'f-1x

Q: consider the product of 3 functions w= f x g x h. Find an expression for the derivative of the…

A: Given functions are f, g , hTheir derivatives are given by f ' , g ' , h '

Q: x2 -4 b) By use derivative sketch the function f(x) %3D 2x

A:

Q: tan x – 2 If f(x) sec x f'(x) = f'(4) =

A: f(x) = (tan x - 2)/sec x f(x) = (tan x/sec x) - (2/ sec x)        = (sin x * cos x /cos x) - (2 cos…

Q: 9) Find f(x) if f'(x) = 7 sin x + 2x - 3 and f(0) = -3

A: Obtain f(x) by integrating the given first derivative as follows.

Q: 4. Differentiate the function. (1) f(x)= in x (2) f(x)= In{x (3) f(x)= In- 2x²(x+2)³ (3x- 2) (4)…

A: HI there, At a time we can answer only one question. So, I have answered first question.

Q: tan x – 4 - If f(x) = sec x f' (x) = f'(1) =

A: We will use relationship between different trigonometric function to solve this.

Q: Verify that f has inverse function then use function f and the given real number a=2 to find…

A: Given information:

Q: 4 Let f(x) =(3/3(2x– 5)' +4- sin (5x* – 2x*)) . Find f (x). %3D |

A: Since I have rechecked my solution 6 times so there is no mistake as far as I know. So please ignore…

Q: Find an anti-derivative for each function in C equals zero

A:

Q: The product rule states that if h(x) = f(x)g(x) then h'(x) = f'(x)g(x) + f(x)g'(x).  In other words…

A: 1) 3 is a constant, it does not depend on x, so we can take 3 out and then apply power rule on just…

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: Find the derivative of the inverse of the given function at the specified point on the graph of the…

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Q: Find the inverse of the function on the given domain. (Enter the domain using interval notation.)…

A: f(x)=(x+4)2-8 To find inverse , replace f(x)by y then swap the variables x  and y .  f(x)=(x+4)2-8…

Q: Find a general formula for f.(n) f(x)=(x-7)-1 Talking about formula to find any derivative

A: Given:

Q: What are the important types of functions frequently encountered in calculus? Give an example of…

A: Some of the important functions encountered in calculus with examples are as follows.

Q: Find (f-1)(a). f(x) = 5 + x + tan(rx/2), -1 < x < 1, a = 5 (f-1)'(a) =

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Q: Show that the function f(x) = |x-3| is not differentiable at x = 3.

A: