(6) its inverse f-1(x) and which are onto R. Determine which of the following mappings f : R →R are one-to-one (if one-to-one, spec (a) f(x) = 3x – 4 (b) f(x) = x²

Let f : R → R be defined as f(x) = x3 + 8(i) Prove that f is a bijection (one-to-one correspondence)(ii) Find the inverse of f.

Determine if the function F is a linear transformation. F:R3 → R² defined by 3x1 + x2 - 6x3 -x1 + x2 + 13x3] F X2

rewrite the function F = (A ⊕ B) ⊕ C without the XOR operator, ⊕.

Let f and g be the functions defined by f: R² → R² (x, y) → and (y,x) g: R² R² (x,y) → (x+3, y — 4). (a) Describe the geometric effect of each of f and g. (b) Determine the composite function go f. (c) Show that g is one-to-one and onto, and determine its inverse function g-¹.

The function f is defined as follows: f: R² → R² with f(x, y) = (2x, x+y) Which statement is correct? f is NOT a linear map and it is not one to one. f is a linear map but it is not injective. f is a linear map and it is injective. f is a NOT a linear map but it is one to one.

Determine a mapping of the form (x, y) → (, ) for the inverse of a relation. a. (x, f(x)) b. (x, y¹) c. (y, f(x)) d. (y, x)

Let ƒ : R → R and g : R → R be the functions given by f(x) = 2x³ + 5 g(x) = √√/1/√(x - 5) Verify that f and g are inverses of one another by showing that go f and fo g both equal idr.

Let f(æ) = (x + 3)². Find the inverse of f restricted to[- 3, 0). f(x) =

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.