Show thatf:R→Rdefined byf(x)=(x−1)(x−2)(x−3)is surjective but not injective. View Solution LetA={x∈R:−1≤x≤1}=B. Then, the mappingf:A→Bgiven byf(x)=x|x|is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) none of these...
i(njective) to indicate that the relation is an injective (but not bijective) function s(urjective) to indicate that the relation is a surjective (but not bijective) function b(ijective) to indicate that the relation is a bijective function ...
Explanation − We have to prove this function is both injective and surjective. If f(x1)=f(x2)f(x1)=f(x2), then 2x1–3=2x2–32x1–3=2x2–3 and it implies that x1=x2x1=x2. Hence, f is injective. Here, 2x–3=y2x–3=y ...
In summary, an injective function is one where each input has a unique output, but not all outputs are covered by the function. For example, the function f(n)=3n defined on the set of natural numbers is injective, but not surjective, as there are some outputs (such as 1) that are ...
if f be a differentiable function such that f(x)=x2∫x0e−tf(x−t). dt. Then f(x) = Ainjective but not surjective Bsurjective but not injective Cbijective Dneither injective nor surjectiveSubmit Question 2 - Select One Let f be a differentiable function with range (0,∞) and g...
A function with this property is called onto or a surjection. Thus, a function with a codomain is invertible if and only if it is both injective (one-to-one) and surjective (onto). Such a function is called a one-to-one correspondence or a bijection, and has the property that every...
(1) We call f injective or an injection if, for s1, s2∈ A s1≠s2⇒fs1≠fs2 or equivalently, if, for s1, s2∈ A, fs1=fs2⇒s1=s2. (2) We call f surjective or a surjection if the image of f is B, i.e. f(A) = B, i.e. for each t∈ B, there exists s∈ A su...
is not an injective, i.e. many-one function. in maths, an injective function or injection or one-one function is a function that comprises individuality that never maps discrete elements of its domain to the equivalent element of its codomain. we can say, every element of the codomain is ...
On a graph, the idea of single valued means that no vertical line ever crosses more than one value.If it crosses more than once it is still a valid curve, but is not a function.Some types of functions have stricter rules, to find out more you can read Injective, Surjective and ...
A function is defined with the rule that a single element in the domain cannot have two different functional values in the codomain. An injective function satisfies one more condition that two distinct elements in the domain cannot have the same image in the ...