very basic verification of pre-image of a function

Question

working with the set $\{(1,2),(2,1),(3,1),(5,4)\}$

I always second guess myself and sometimes confuse myself over simple things. The question asks whats the pre-image of $f^{-1}(1)$.

My answer is that the pre-image is $(2,3)$ since $2,3$ in domain both map to $1$ in the codomain

Is the set that you've given that of the inverse of $f$ or that of $f$ itself? — jl00, Jan 19 '20 at 02:22

score 1 · Accepted Answer · answered Jan 19 '20 at 02:33

1

The pre-image of a function $f^{-1}(y) = \{x:f(x)=y\}$. In this case since $(2,1)$ and $(3,1)$ are in the function then the pre-image of $1$ is $\{2,3\}$.

answered Jan 19 '20 at 02:33

CyclotomicField

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very basic verification of pre-image of a function

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