Question A: If the function f is continuous on [2,1] and f(2) = 1, f(0) = ?2 and
ID: 3285445 • Letter: Q
Question
Question A: If the function f is continuous on [2,1] and f(2) = 1, f(0) = ?2 and f(1) = 0, is it possible that f is one-to-one? If the answer is yes, give an example of a one-to-one function satisfying these conditions. If the answer is no, provide a justification that any function satisfying these conditions cannot be one-to-one. Question B: Find all values of x such that the tangent line to y = 4x2 + 11x + 12 is steeper than the tangent line to y = x3. Find all values of x such that the tangent line to y = 4x2 +11x+12 is parallel to the tangent line to y = x3. Find all values of x such that the tangent line to y = 4x2 + 11x + 12 is shallower than the tangent line to y = x3. Interpret your solutions geometrically.Explanation / Answer
ANSWER IS YES Function is a relation between output and input.Output depends upon input. As the input of a function changes the output also changes.Let a function is f(a) = b then a is the input and b is the output. Set of all input is domain and set of all output is range or co-domain. Function is defined as follows, "function is a relation between domain and range. Considering two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B. When a relation satisfies this rule, it is called a function." In this chapter, we will study how a function is a relation, but a relation may not be a function. Hence, the function calculator sections helps to differentiate relation and a function. If f is a function from A ? B and defined as f(a) = b then a = A and b = f(a) = B is unique. A is domain and B is co domain or we can call it as Range of function f. Also, we can say that f from A to B is a relation and every relation from A to B is not a function. Note: f is a set of ordered pairs, no two of which have the same first coordinate. The general notation of a function is y = f(x). It is also denotes as f : X ? Y where, f is the function defined between X and Y where, x is in X and y is in Y. Characteristics of FunctionsBack to Top Below are the characteristics of functions: Two functions f,g are equal if and only if they have same domain and range"> domain and range and f(x) = g(x) for every x = A f: A ---> B is one-one(Injection) if and only if for all a0 ,a1 = A,