Question

Consider the following functions, where I and J denote two subsets of the set R of real numbers.

f: R→R x→1/√(x+1)

f_(I,J): I→J x→ f(x)

(a) What is the domain of definition of f?

(b Let y be an element of the codomain of f. Solve the equation f(x)=y in x. Note that you may have to consider different cases, depending on y.

(c) What is the range of f?

(d) Is f total, surjective, injective, bijective?

(e) Find a pair (I,J) such that f_(I,J) is bijective and its range is the range of f. What is then the inverse of f_(I,J)

Answer 1

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