Why Is E^x Not Surjective?

Why is it not surjective? The solution says: not surjective, because the Value 0 ∈ R≥0 has no Urbild (inverse image / preimage?). But e^0 = 1 which is in ∈ R≥0.

Why is X not surjective?

You have not specified the domain and codomain of the your function. In fact, it is onto when you consider it as a function from R to [0,∞). However, it is not onto when considered as a function from R to R as there does not exist a pre-image for any x<0.

Why is exponential function not surjective?

The function g : R → R defined by g(x) = x2 is not surjective, since there is no real number x such that x2 = −1. ... Its inverse, the exponential function, if defined with the set of real numbers as the domain, is not surjective (as its range is the set of positive real numbers).

James H. Sterling

James H. Sterling

Environmental Science & Climate Journalist

James Sterling reports on renewable energy developments, climate policy, ecological conservation, and green tech innovations around the globe.