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Dᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ᴘᴏɪɴᴛs ᴏғ ᴄᴏɴᴛɪɴᴜɪᴛʏ ᴏғ ᴛʜᴇ ᴄᴏᴍᴘᴏsɪᴛᴇ ғᴜɴᴄᴛɪᴏɴ ʏ = ғ[ғ(x)], ɢɪᴠᴇɴ ᴛʜᴀᴛ, ғ(x) = 1/x-1.
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Dᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ᴘᴏɪɴᴛs ᴏғ ᴄᴏɴᴛɪɴᴜɪᴛʏ ᴏғ ᴛʜᴇ ᴄᴏᴍᴘᴏsɪᴛᴇ ғᴜɴᴄᴛɪᴏɴ ʏ = ғ[ғ(x)], ɢɪᴠᴇɴ ᴛʜᴀᴛ, ғ(x) = 1/x-1.
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Answer:
g(x) is continuous ∀ x ∈ R-{2}
Explanation:
Let g(x) = f(f(x))
∴ g(x) is given by
Now Since g(x) is a polynomial function, it is continuous at all points except at x=2.
Because at x=2; g(x) is not defined
∴ g(x) is continuous ∀ x ∈ R-{2}
Hope this asnwer helped you :)