Exercise 6: Suppose f and g are functions such that: -3 f = 1, i=7, f = 5, -3 Г» g = 6, g = 3, :-4. Compute the following. (a) f (b) / . -3 (c) -3 (d) / f(x)+g(æ)dx (e) f(«) — 29(х)dx

Q: find (f o g) (2): f(x) = x^2 + 1, g(x) =x -1

A: (f o g) (2) = f(g(2)) So we will find g(2) by plugging x=2 in g(x) g(x)=x-1 g(2)=2-1 g(2)=1

Q: f(x) = x²-6x+5, what is the domain of the inverse of the function  (f^(-1))?

A: f(x)= x2 -6x +5 f(x)= y= (x-3)2-4 Graph of f: f(x)= (x-3)2-4 is an upward parabola having veterc at…

Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: Show that f-(A U B) = f-'(A) U f-'(B) and f-1(A n B) = f-'(A) nf-'(B) for any function f. Is the…

A:

Q: Determine whether z^5-4iz^3+(1+8i)z+(17+(i)^(1/2)) is an entire function? Justify your answer

A: yes it is entire function.Explanation:Step 1:Step 2:Step 3:

Q: Use the graph below to fill in the missing values. f(x) -1 4 f(0) = f(«) — 0, х 3 f -'(0) = f («) —…

A: To find f(0) we find y when x=0 At x=0, y=4 So, f(0)=4

Q: y= +1) %3D

A: Given y=x(x2+1)4 Differentiate with respect to…

Q: Determine f '(x) for the function

A: The derivative of the function is computed as follows.

Q: es of f'(-7), f'(-4) & f'(-2)

A: at x= -7 graph is increasing At x = -4 graph gives local Maxima At x = -2 graph is decreasing

Q: Find the inverse function of f. f(x) = x³- 9 O s-'x) = Vx+9 %3D O f-'x) = Vx+ 9 O 5-x) = Vx- 9 O…

A: Given function fx=x5-9. The objective is to find the inverse function of f.

Q: Fnd f'Ce) of the fallowing functien. f Cx)

A:

Q: Consider the function f(x)=ln⁡(x2+3x−10) Find the domain of the function f(x) and enter your domain…

A:

Q: Let f(x) = 5x - 2 and g(x) = 2- x^2. Find the following. A) g(f(3)) B) f(g(x)) C) ff(x))

A:

Q: Find inverse function of (a) y = - x^2 (b) y = 3 - 2x

A:

Q: Find the inverse function of y = (2x-1) (x-1) fx) = -1) 2x f(x) =2* fx) = (x+1) 2x (х-1) fx) = (x+1)…

A: Inverse of the function

Q: Graph the pair of functions and identify the transformation of f(x) that produces g(x). S(x) =lx|-2,…

A: To identify: The transformation of fx that produces gx. Given: The functions are fx=x-2 and gx=-x+2.…

Q: The inflection point of the function f(x) = x³ – x² + 5x +1 is: 70 (3, 27 70 (-3,–) 27 (-3 70 (-3,…

A: Given function is fx=x3-x2+5x+1

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: h (x) = x" – xV2

A: We have to differentiate the function: hx=xπ-x2 We know the formula of differentiation,…