Which function below is the inverse of f:R-{2} → R-{3} ut of f(x)= -3x+1 X X-2...
2) (12) f:R-(3/2)-R-10, (x) 1/(3 2x) g:R--21->R-1o), g (x)1/ (x 2) h:R-(-4/3]-R-(1/3), h(x) (f o g) (x) Verify if h(x) is one to one and onto. If it is, find the inverse function of h(x). 2) (12) f:R-(3/2)-R-10, (x) 1/(3 2x) g:R--21->R-1o), g (x)1/ (x 2) h:R-(-4/3]-R-(1/3), h(x) (f o g) (x) Verify if h(x) is one to one and onto. If it is, find the inverse function of h(x).
10) (4 points) Prove or disapprove the function f:R → R such f(x) = 3x - 2 is one-to-one?
Select the correct answer. What is the inverse of function f? 3 – I 7 OA. -1(x) = 3 – 7x OB. +(x) = 3 - OC -1(1) = ? OD. 7-1(x) = 74 – 3 7+ I 3 3 Select the correct answer. Find the inverse of function f. f(x) = 12 +7 IN A f(x) = 2x + 3 OB. F'(x) = 2x - 7 OC. (n) = 2x – 14 OD. F'(x) = r - 7 Type...
14. Find the inverse function of f(x) = (x-5)3 f-1x= 3x -5 f-1x= 3x +5 f-1x= x+5 f-1x= 3x +125 f-1x= 3x -125 15. Find the center and the radius of the circle (x-4)2+(y+3)2 =64. (4, -3), r = 8 (-3, 4), r = 8 (-4, 3), r = 64 (-3, -4), r = 64 (-4, -3), r = 64
cewise Functions e function, evaluate lim f(x). 2 1-2x²+x+3 f(x) = { 2x2 – 3x + 3 (-3x - 2 if if xs1 1<x< 6 if x26 below:
1. Let f:R → R be the function defined as: 32 0 if x is rational if x is irrational Prove that lim -70 f(x) = 0. Prove that limc f(x) does not exist for every real number c + 0. 2. Let f:R + R be a continuous function such that f(0) = 0 and f(2) = 0. Prove that there exists a real number c such that f(c+1) = f(c). 3 Let f. (a,b) R be a function...
7. Consider the function f:R + R defined by f(x) = x < 0, 3 > 0. e-1/x2, Prove that f is differentiable of all orders and that f(n)(0) = 0 for all n e N. Conclude that f does not have a convergent power series expansion En Anx" for x near the origin. [We will see later in this class that this is impossible for holomorphic functions, namely being (complex) differentiable implies that there is always a convergent power...
(2) Consider the function f given by f:R R f(a)1 2 (a) Determine the domain D and range R of the function f. (b) Show that f is not one to one on D. (c) Let ç D be a subset of the domain of f such that for all x ? S, 0 and the function is one to one. Find such a set S. (d) For the set S given in Part (c), find f (x) (e) Determine...
(c) Find a formula for the inverse of the function. 4x-1 ) f(x) _[3 marks] 2x+3 (ii) f(x) = /10 - 3x [2 marks) 1+1 (111) g(x) = 1-e* [3 marks] Total: 25 marks!
find the inverse of f-1(x) of the function f(x)= ^3 root x-5 3) find the inverse f(x) of the function, f(x) = 3JX-5 3x = 14-5 deel X² = Jy - 5