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ใ„ใ„ใˆใ€‚ใ™ในใฆใฎ้–ขๆ•ฐใซ้€†้–ขๆ•ฐใŒใ‚ใ‚‹ใ‚ใ‘ใงใฏใ‚ใ‚Šใพใ›ใ‚“ใ€‚้–ขๆ•ฐ f: X โ†’ Y ใŒ้€†้–ขๆ•ฐใ‚’ๆŒใคใซใฏใ€Y ใฎไปปๆ„ใฎ y ใซๅฏพใ—ใฆใ€ใกใ‚‡ใ†ใฉ 1 ใคใฎ x ใŒๅญ˜ๅœจใ—ใฆ f(x) = y ใจใชใ‚‹ๅฟ…่ฆใŒใ‚ใ‚Šใพใ™ใ€‚ใ“ใฎๆ€ง่ณชใŒๆบ€ใŸใ•ใ‚Œใฆใ„ใ‚‹ๅ ดๅˆใ€้–ขๆ•ฐ g: Y โ†’ X ใŒๅญ˜ๅœจใ—ใฆใ€f ใจใฎ้–“ใซๅฟ…่ฆใช้–ขไฟ‚ใŒๆˆ็ซ‹ใ—ใพใ™ใ€‚
ใ„ใ„ใˆใ€‚
if a function is not one to one does it have an inverse
Not all functions have inverse functions. In order for a function f: X โ†’ Y to have an inverse, it must have the property that for every y in Y there must be one, and only one x in X so that f(x) = y. This property ensures that a function g: Y โ†’ X will exist having the necessary relationship with f.
้–ขๆ•ฐใŒใ„ใฃใ•ใ„ๅ˜ๅฐ„ใงใชใ„ใชใ‚‰ใฐ้€†้–ขๆ•ฐใŒๅญ˜ๅœจใ™ใ‚‹ใ‹