Determine and justify whether the following mappings are one to one, onto or both
Determine and justify whether the following mappings are one to one, onto or both Owl rmine...
For each of the following functions, determine whether or not they are (i) one-to-one and i) onto. Justify your answers (a) f : R-{0} → R and f(x) = 3r-1/x (b) g : R _ {1} → R and g(x) = x + 1/(x-1) (c) l : S → Znon-reg and l(s) = number of 1's in s, for all strings s E S, where s is the set of all strings of O's and 1's. (d) 1 : S...
For each of the following functions, state whether or not the function is one-to-one, onto, both, or neither: 1) f : Z → Z defined by f(x)=2x + 1; 2) f : R → R defined by f(x)=2x + 1;
7. Determine whether each of these functions is one-to-one or onto. (a) f:Z + Z, f(n) 3n +1.
Question is in the description!! Problem 2. Determine whether the followings transformations are one-to-one, or onto, or both, or neither 418 8r2 (2) T : Rs → R, 지미 ) 1 -22 |12-2x3 r3, r1-2r2
2. Determine whether the following equations are linear in r, y and z: justify your answer.
Suppose T:R4_R4 is the transformation given below. Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a vector in R4 that is not in the range of T. 2x0+6x1+6x2+4x3 -2x0–x1-x2 + x3 |-3x0-8x1-5x2+4x3 xo+5x1+6x2+7x3 2 Tis one-to-one Tis onto
Suppose T:R3-R3 is the transformation given below. Determine whether I is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a vector in R3 that is not in the range of T. хо 3x0-3x4–3x2 3x0-3x1 x2 X0-X1-3x2 TX1 = T is not one-to-one: 0 0 0 0 TO = and TO 0 0 0 0 T is not onto:...
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
Question 7 Determine whether the linear transformation T is one-to-one and whether it maps as specified. 2 + 3x 3) T(X 1, X 2, x 3) = (-2x 2 - 2x 3, -2x 1 + 8x 2 + 4x 3, -X 1 - 2x 3,3x Determine whether the linear transformation T is one-to-one and whether it maps R 3 onto R4. Not one-to-one; not onto R4 One-to-one; onto R4 Not one-to-one; onto R4 One-to-one; not onto R4
Determine whether the linear transformation is one-to-one, onto, or neither T: R^2 -> R^2 , T(x,y) = (x-y,y-x)