i) the inverse of a function can exists if, and only if, the function f (x) is a one-one mapping ii) the domain of f (x) is the domain if f^-1(x) iii) the graph
Matematika
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Pertanyaan
i) the inverse of a function can exists if, and only if, the function f (x) is a one-one mapping
ii) the domain of f (x) is the domain if f^-1(x)
iii) the graph f (x) & f^-1(x) are reflections of each other in the line y=x
which statement is true?
ii) the domain of f (x) is the domain if f^-1(x)
iii) the graph f (x) & f^-1(x) are reflections of each other in the line y=x
which statement is true?
1 Jawaban
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1. Jawaban ShanedizzySukardi
Subject Function
Statement (i) is wrong. The correct one is that the inverse of the function exists if and only if the function mentioned is bijective function (one-to-one correspondence)
Statement (ii) is wrong. The domain of f(x) is the codomain of [tex] f^{-1}(x) [/tex]
Statement (iii) is wrong.
[tex] f(x) = x \Rightarrow f^{-1}(x)= x [/tex], while y = x and x = y is the same precise equation. The lines are conjoined and hence don't imply what the reflection means.