The function f(x) = x4 is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of the new function.

Q: For each of the above functions, prove that f(f-1(x)) = f-1(f(x)) = f(x) = +6 f(x) = x3 + 2 f(x)…

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Q: The function f(x) = x? is transformed to 2 -(x + 4)² – 2 g(x) = -- Select all of the transformations…

A: Given

Q: Express the given function h(x) = l3x - 4l as a composition of two functions f and g so that h(x) =…

A: Given :h(x) = 3x -4To express h(x) as a composition of two function f and g so that  h(x) = (f∘g)(x)…

Q: The graph of the continuous function g, the derivative of the function f, is shown above. The…

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Q: Suppose H (x) = (2-2x)*. Find two functions f and g such that (f og) (x)=H(x).

A: H(x)=(fog)(x)=f(g(x))

Q: Find an equation for f(x) using the tangent function. f(x) = f(x) 12- 10 8. 6. 4 2 X 3 2 6. 6 3 6 -8…

A: The given graph is:   To find the equation for f(x).

Q: Draw the graph of the given function. 1. f: R → Z, defined by f(x) = [2x – 3] 2. f : Z → Z, defined…

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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: if f(x) is a function with derivative f'(x)= (x^2 + 1)^5, then the following is true about f(x)

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Q: If f and g are both odd functions, is their product necessarily odd, even or neither? Prove it

A: Given data: *f and g are both odd function. By the definition of the odd function if a function f(x)…

Q: 1. Differentiate the following functions: a) f(x) = 43x²

A: We have to differentiate of the given function

Q: determine the indicated functional values. If f (x) = 4x2 - 1 and g(x) = 4x + 5, find ( f ᵒ g)(1)…

A: Given that, fx=4x2-1gx=4x+5

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…

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Q: Determine analytically if the following functions are even, odd or neither. f(x) = x 2 − x – 6…

A: topic - functions

Q: Find the domain and sketch the graph of the function.

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Q: Find two functions fand g such that h(x) = (f 0 h(x)=√√5x-1 g)(x).

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Q: x, if -1くx<

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Q: Show that f (x) = x + x -1 is one-to-one on [1, ∞ ), and find the corresponding inverse f-1. What is…

A: Given function is: fx=x+x-1 We have to prove that f is one-to-one. Let f(x) = f(y) Then we get,…

Q: The inverse of the function f(x) = +3 is f-'(x) =. O 5(x – 6) 25(x – 3) O 35(x – 3) O 10(x – 3) 5(г…

A: We will find the inverse function as following.

Q: The function f(x)=|x| is not one-to-one. Find a suitable restriction on the domain of f so that the…

A: Function gives a definite relation between set of outputs and inputs. Domain is the set of a values…

Q: For each of the piecewise-defined functions in determine whether or not the function is one-to-one,…

A: Given  The function is f(x)=x    when x&lt;02x  when x≥0

Q: Determine the new value of the function f(x) =x+ Inx if the independent changes from x=2e to x=2.2e

A: Given f(x) = x + ln(x)Value of function at x = 2ef(2e) = 2e + ln(2e) = 2e+1+ln2

Q: Show that f is strictly monotonic on the given interval and therefore has an inverse function on…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Define H(x) as a piecewise defined function and evaluate H(1), H(2), H(3), H(0) and H(-2) given by,…

A: We have to solve the problem by just putting the value in the piecewise function.

Q: The graph of the function f is given below. f is not differentiable at

A: For differentiability of a function,  Left hand derivative = Right hand derivative  That is :

Q: Let f and g be the functions, their sum and difference are denoted by ____________ and ____________…

A: In this question, we have given two functions given as f and g To find their sum and difference

Q: find functions f and g so that f ∘ g = H.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: The parent function f(x)=x² is related to g. Describe the sequence of transformations from f to g.…

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Q: Suppose f- is the inverse function of a differentiable function fand let  G(x)  = 1/f-1(x). If f(3)…

A: Let us assume the g is the inverse of function f. Now, f(x)=g-1(x)g{f(x)}=x Differentiate the above…

Q: Calculate the output for the function with he given input. If there is no possible output for the…

A: The given function isfx=xx-1. Here function fx is not defined if x-1=0. x-1=0x=1 So, the function is…

Q: Find the domain and sketch the graph of the function.

A: fx=x+2    if x≤-1x2        if x&gt;-1 The domain of given function is the set of all real numbers.

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: determine the indicated functional values. If f (x) = -x3 and g(x) = |2x + 4| , find ( f ᵒ g)(-1)…

A: f(x) = -x3  g(x) = |2x + 4|  (f ᵒ g)(-1) = ? (g ᵒ f )(-3) = ?

Q: differentiate the following function: 1. f(x)=3-2x+4x^2 2.  3.

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Q: Suppose thatf and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = -1,…

A: Given :hx = x2+1gx

Q: Determine if the given function is differentiable at a = 1 4 – 2x, if x 1

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Q: Find all values of x such that f (x) &gt; 0 and all x such that f (x) &lt; 0, and sketch the graph…

A: f(x)=x4-4x2=x2x2-4f(x)&gt;0⇔x2x2-4&gt;0⇔x2&gt;0 and x2-4&gt;0 or  x2&lt;0 and x2-4&lt;0⇔x∈ℝ \ 0 and…

Q: Determine whether the following 1 function is continuous at the given point x = 2 2x2 + 9x – 5 1 -…

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Q: Evaluate the piecewise function at the given values of the independent 2x + 4 if x< 0 f(x) = 4x +6…

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

A: To find: Critical points of g where g'(x)=x2-16x-2,x≠2.

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: Given that f(x)=√(6x−15)+10 where f(x)=y, define a function rule for f^−1. Given that…

A: f(x)=6x-15+10 To find out inverse , first we replace f(x) by y y=6x-15+10solve for xSubtract 10 from…

Q: let f be the function given by f(x)=kx/(x^2+1), where k is a constant.  For what values of k, if…

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Q: (3x, if x 0

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Q: 1. Sketch the reciprocal of the function f (x) = x - 6.

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Q: determine the indicated functional values. If f (x) = √(x + 6) and g(x) = 3x - 1, find ( f ᵒ g)(-2)…

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Q: determine the indicated functional values. If f (x) = -5x + 1 and g(x) = √(4x + 1), find ( f ᵒ g)(6)…

A: Given functions - f(x) =-5x+1            ..........(1)g(x) = 4x+1           ..........(2)Part (a) -…