Suppose that f: X→Y and g: Y→Z are functions. Please teach me how to write the convers and inverse of the following statement. And what is a counter example of the converse? If both f and g are one-to-one, then g(f(x)): X→Z is one to one.

Q: Consider the following function, f(x) = x³, 3 a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate

A:

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: Suppose g(x) = f(x) + k. Identify a value of k that transforms f into g. k =

A:

Q: Which of the following functions is not one-to-one? (a) f(x) = x³ on (-00, 00) (b) f(x) = x² on (-0,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Differentiate the following with respect to x: f(x) = x³In (x)

A:

Q: Determine whether the following function is continuous at the given point 1 = 2x+11x f(z) = 2x 13

A:

Q: do you agree with the contention that the functions f(x) = x+2 and g(x)=x2-4 /x-2 are the same in…

A: It is given that, f(x) = (x+2)     and     g(x) = ( x2-4)/(x-2) Then we will prove that f(x) and…

Q: The function h(x)=1/x−4, can be expressed in the form f(g(x)), where g(x)=(x−4), and f(x) is defined…

A: Given: ------------------------------------------------------------------------------------------…

Q: Find the inverse of the bijective functions below: a) f: R+ → R*, defined by f(x) = x² . %3| b) f:…

A: Find your answer below

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

A:

Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x. ( x2…

A: It is given that y is implicitly a function of x. =x2+y23/2 differentiate with respect to x

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

A: We have to differentiate of the given function

Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x.…

A:

Q: Consider the following function. Find the f(x) = %3D x+3 3x = (x), 1=x %3D

A:

Q: x, if -1くx<

A:

Q: Consider the following functions. f(x) = x², g(x) = x + 5 %3D

A: Givenf(x)=x2 , g(x)=x+5

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: Show that the following function is nowhere analytic. f(2) = 2xy + i(x² – y³) %3D

A: Function is said to be analytic at a point if there is a nbd of the point such that f is…

Q: The inverse of the function f(x) = is f-'(x) =_ x + 3 (3x + 4) (1 – æ) (3x – 4) (5 – x) O (3x + 4)…

A: Let y = f(x)

Q: Express h(x) as a composition of two functions:    h(x) = ∛( x2 + 1).

A: Given: h(x)=x2+13 To find: The composition of two function. That is h(x)=f(x)∘g(x)

Q: Consider the following two functions: In(x + 3) and x 0.4 Which function dominates as 0.4 0.4 00?…

A: Given that: Two funcitons: ln(x+3) and x0.4

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: (г,9) —(0,0)22 — у4 – y4

A:

Q: x² +2x+1, if x -2

A:

Q: Differentiate the following function. f(x) = 186.1

A:

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

A:

Q: Consider the following functions. f(x) = √√√√64 - x², g(x): = √x + 2

A:

Q: Consider the functions: f (x) = 3x – 1; g(x) = 1– 2x Compute fo g(-26) exactly

A: The given function is  f(x) = 3x-1  g(x) =1-2x  We have to calculate f(g(-26)).

Q: 8. Analyze the differentiability of the following function: f(t) = Vx² – 2 State the restrictions in…

A:

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

A:

Q: 0.4x + 0.2, x 2 -

A: The given function f(x) is, f(x)=0.4x+0.2x&lt;21x=21.8x-2.6x&gt;2 A function is said to be continues…

Q: Suppose that f(x) is differentiable function such that f' (1)=8 and f (1)=4. If    g(x) = (f(x)) /…

A:

Q: Suppose that f(x) is a differentiable function such that f(8)=5 and f(8)=0. If g(x)=sin(f(x)), then…

A:

Q: Prove that if f(x)=c (a constant function), then f'(x)= 0

A: Given query is to prove that derivative of constant function is zero.

Q: If f(x) = |x| + |x – 1| and g(x) is the piecewise function defined by: 2r-1 x> 1 0<x<1 1- 2r x<0…

A:

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: Consider the following functions f (x) =x² – 1 and g (x) = 2 – 2 Evaluate fog(-4)

A: Given data: fx=x2-1 gx=2-x Solution: Calculation of g-4 g(x)=2-x g(-4)=2-(-4) g(-4)=-6

Q: Select the function that has a well-defined inverse. Of:Z Z f(x) = 2x – 5 Of:Z Z f(x) = [x/2] Of:Z→…

A: Option (d) has a well-defined inverse. Thus option (d) is correct.

Q: Let h(x)=f(x)g(x). If f(x)=2x2+1,g(1)=0, and g′(1)=−1, what is h′(1)?

A:

Q: Consider the following function. f(x) = { 35 4x – 1 if x 1

A: We will use the fact that

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: Consider the following functions. f(x) = 9x − 8,   g(x) = x/3

A:

Q: iy, whether the following functions are one-to- nd draw the function and its inverse on the sam 2 +…

A: We have to find the following given conditions according to the given condition

Q: (3x+5, f (x) =. | if x 2 5 if xく5 ーx+ 3,

A:

Q: The inverse of the function f(1) is f-(z) =. %3D O (5z – 9) (1+1) O (5x – 9) (5 – z) (1 – z) (5z +9)…

A:

Q: What values of a and b will make the function f continuous at x=2 and x=3? * x2 - 4 if x 3 2x – a…

A:

Q: The inverse of the function f(x) is f'(x) x + 5 (1 – æ) (5л + 9) (5л + 9) (1 – 2) O (5x + 9) (1+x)…

A: