show that the function f:N-N defined by f(m)=m^2 +2m+3 is one one but not onto
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ʙᴜᴛ ᴡᴇ ᴋɴᴏᴡ, ɪꜰ ᴀʀᴇ ꜱᴜᴄʜ ᴛʜᴀᴛ ꜰ(ᴀ) = ꜰ(ʙ) ᴀ =ʙ, ᴛʜᴇɴ ꜰ ɪꜱ ᴏɴᴇ-ᴛᴏ-ᴏɴᴇ ꜰᴜɴᴄᴛɪᴏɴ ᴏʀ ɪɴᴊᴇᴄᴛɪᴠᴇ ꜰᴜɴᴄᴛɪᴏɴ. ᴛʜᴇɴ, ꜰ ɪꜱ ꜱᴜʀᴊᴇᴄᴛɪᴠᴇ ᴏʀ ᴏɴᴛᴏ ꜰᴜɴᴄᴛɪᴏɴ. ʜᴇɴᴄᴇ, ɢɪᴠᴇɴ ꜰᴜɴᴄᴛɪᴏɴ, ꜰ ɪꜱ ᴀʟꜱᴏ ꜱᴜʀᴊᴇᴄᴛɪᴠᴇ ᴏʀ ᴏɴᴛᴏ ꜰᴜɴᴄᴛɪᴏɴ. ɴᴏᴡ ɪᴛ ɪꜱ ᴘʀᴏᴠᴇᴅ ᴛʜᴀᴛ ᴀ ꜰᴜɴᴄᴛɪᴏɴ ɪꜱ ɪɴᴠᴇʀᴛɪʙʟᴇ ꜰᴜɴᴄᴛɪᴏɴ ɪꜰ ᴀɴᴅ ᴏɴʟʏ ɪꜰ ɪᴛ ɪꜱ ᴏɴᴇ ᴛᴏ ᴏɴᴇ ᴀɴᴅ ᴏɴᴛᴏ.
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A black hole is a region of spacetime where gravity is so strong that nothing—no particles or even electromagnetic radiation such as light—can escape from it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole.
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