The function f : R → R is defined by the rule f(x)=2x+3              a. Prove f(x) is one to one             b. Prove f(x) is onto   2. Give a counterexample to show that the function h: Z → Z, defined by the rule h(x)=2x+3, is not onto.

Q: 1. Let f : Z6 → Z6 be such that f(7) = x2 + 3. (a) Is f a well defined function? (b) Is f…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: The function f from R to R is defined as f (x) = x²(x − 1), determine (a) whether f is one to one.…

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Q: Let f:R → R such that f(x) = x² – 2x + 1. Verify whether f is bijective ? explain your answer.

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Q: 2. Let f: A → B and g: C → D be functions. The product of f and g is the function defined as…

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Q: Let ƒ : R\{1} →→ R\{1} be defined by f(x) = x/(x - 1). Show that ƒ is bijective and find f-¹. Also,…

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Q: Give an example of a function f : (X1, d1) → (X2, d2) that sends compact sets to compact sets, but…

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Q: 4. Define the operators T and U on the space P(R) of all polynomials in variable x as follows:…

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Q: Let f: A → B be a function and let a ∈ A and b ∈ B. Does this mean it is true that f(a) = b? If not,…

A: We use definition of function .

Q: (5) Within real numbers, let A = {x: 0<x< 1} and B = {r: 0<x< ∞}. Define f : A → B by f(x) = 1. Show…

A: A function f(x) from A to B is said to be bijective iff f(x) is both injective and surjective. To…

Q: Let X, Y and Z be sets. A, B are subsets of Y. f:X → Y is a function. Prove the given statement if…

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Q: 6. Let f(x) = x55x+1. Prove that f has at least 3 zeros in [-2, 2]; that is, there exist distinct…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.