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If ๐‘“(๐‘ฅ)=๐‘’๐‘ฅ and ๐‘”(๐‘ฅ)=4๐‘ฅ2โˆ’1, find ๐‘“(๐‘”(๐‘ฅ)).๐‘“(๐‘”(๐‘ฅ))=

Question

If ๐‘“(๐‘ฅ)=๐‘’๐‘ฅ and ๐‘”(๐‘ฅ)=4๐‘ฅ2โˆ’1, find ๐‘“(๐‘”(๐‘ฅ)).๐‘“(๐‘”(๐‘ฅ))=

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Solution

To find the composition of two functions, ๐‘“(๐‘”(๐‘ฅ)), you substitute ๐‘”(๐‘ฅ) into ๐‘“(๐‘ฅ).

Here, ๐‘“(๐‘ฅ) = ๐‘’^๐‘ฅ and ๐‘”(๐‘ฅ) = 4๐‘ฅ^2 - 1.

So, ๐‘“(๐‘”(๐‘ฅ)) = ๐‘“(4๐‘ฅ^2 - 1) = ๐‘’^(4๐‘ฅ^2 - 1).

So, ๐‘“(๐‘”(๐‘ฅ)) = ๐‘’^(4๐‘ฅ^2 - 1) is the composition of the two functions.

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