Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4). y 6 5 + 3 2 1 1 (2,4) 2 3 Orq g 4 f 5 (6, 6) (6,5) 6 7

Q: The equation of a quartic function with x-intercepts at 1 (order 2), -3 (order 1), 2 (order 1) and…

A: Let's find.

Q: Let P = (x, y) be a point on the graph of y = Vx. Express the distance d %3D from P to the point (1,…

A: Any point P(x,rootx). From that we got answer.

Q: Suppose that f(x) is a function with f(155)=70 and f′(155)=1. Estimate f(157

A: topic -  line and differentiation

Q: Find G'(w) if G(w) = 9 6 4w +6+ √w.

A:

Q: g(x) = V4t + 5dt. Find g'(2). Let 3-x

A: We have given that  gx = ∫3-xx24t+5dt We have to find g'2 for that we have to use Leibniz integral…

Q: For y = f(x)=x² - 2x +9, find dy and Ay, given x = 1 and Ax = -0.1.

A: Given,            y=f(x)=x2-2x+9. and  x=1, ∆x=-0.1. To find dy and ∆y.

Q: Given the function f(x, y) = x²y4 - In (xy), find fx(1, 1) and fy(1, 1)

A:

Q: Let h(x)=f(g(x)). If f(−4)=−3, f′(−4)=−1, g(1)=−4, and g′(1)=3, find h′(1).

A: The formula one have to use here is f(g(x))'=f'(g(x))* g'(x)

Q: Suppose f: R → R is a function such that for all x, y ≤ R, f(x + y) = f(x) + f(y) and f(xy) =…

A:

Q: Let f(x) = x – 5, g(x) = /x , h(x) = x°, and j(x) = 3x. Express each of the functions given below as…

A: The solution of above question is written in below steps.

Q: Given that h(x) = ƒ(g(x)), find h′(3) if g(3) = 4, g′(3) = 5,ƒ(4) = 9, and ƒ′(4) = 10.

A:

Q: et h(x)=f(g(x)). If g(−2)=3, g′(−2)=−1, f(3)=−5, and f′(3)=−6, find h′(−2).

A: Given function is : hx=fgxg-2=3g'-2=-1f3=-5f'3=-6   To find the value of h'-2

Q: , v(0) = and Find the position function, F(1), given that F(0) = a(t) = .

A: We have to find position vector

Q: Let u and v be the linear functions defined asu(x)=2x+3,v(u)=3x-2.Find the compositions u*v and v*u.…

A: For uov, we do u(v(x)), and for v o u, we do v(u(x)) .

Q: 3 If f(x) = Vx and g(x) = x° – 23, simplify the expressions (fo g)(3), (f o f)(4), (g o f)(x), and…

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

Q: (x) - provided

A: To fill the given blanks.

Q: 4. Find the functions f(x), g(x),h(x) that satisfy: f(g(h(x))) = 2.

A: A composite function is created when one function is substituted into another function .

Q: Suppose F′′(x)=Ax+B, with F′(1)=r and F(1)=s. Find F′(x) in terms of A, B, and r. F′(x)= Now find…

A: given  F''(x)=Ax+BF'(1)=r and  F(1)=sF'(x)=∫(Ax+B)dx∫xndx=xn+1n+1+c

Q: functions identical?

A:

Q: 4. Consider the function f(x)=√x-1. Find f-¹(x) and sketch the graphs of y = f(x) and y = f(x) on…

A: Given that the function fx=x-1. Find the inverse function f-1x. Sketch the graph of y=fx and y=f-1x…

Q: If (f°g)(x)=2x-1,how might f(x) and g(x) be defined?

A: (f°g)(x)=2x-1 can be written as f(g(x)) So g(x) is the inner or the first function  And f(x) is…