Select the correct answer.Which function defines (๐โ ๐)โข(๐ฅ) ?๐โก(๐ฅ)=log(5โข๐ฅ)๐โก(๐ฅ)=5โข๐ฅ+4 A. (๐โ ๐)โข(๐ฅ)=5โข๐ฅlog(5โข๐ฅ)+4 B. (๐โ ๐)โข(๐ฅ)=5โข๐ฅ+4+log(5โข๐ฅ) C. (๐โ ๐)โข(๐ฅ)=5โข๐ฅโ4โlog(5โข๐ฅ) D. (๐โ ๐)โข(๐ฅ)=5โข๐ฅlog(5โข๐ฅ)+4log(5โข๐ฅ)
Question
Select the correct answer.Which function defines (๐โ ๐)โข(๐ฅ) ?๐โก(๐ฅ)=log(5โข๐ฅ)๐โก(๐ฅ)=5โข๐ฅ+4 A. (๐โ ๐)โข(๐ฅ)=5โข๐ฅlog(5โข๐ฅ)+4 B. (๐โ ๐)โข(๐ฅ)=5โข๐ฅ+4+log(5โข๐ฅ) C. (๐โ ๐)โข(๐ฅ)=5โข๐ฅโ4โlog(5โข๐ฅ) D. (๐โ ๐)โข(๐ฅ)=5โข๐ฅlog(5โข๐ฅ)+4log(5โข๐ฅ)
Solution
The correct answer is A. (๐โ ๐)โข(๐ฅ)=5โข๐ฅlog(5โข๐ฅ)+4.
Here's why:
The notation (๐โ ๐)(๐ฅ) represents the composition of the functions ๐ and ๐, which means you first apply function ๐ to ๐ฅ, and then apply function ๐ to the result.
Given ๐(๐ฅ)=log(5๐ฅ) and ๐(๐ฅ)=5๐ฅ+4, the composition (๐โ ๐)(๐ฅ) would be ๐(๐(๐ฅ)).
Substitute ๐(๐ฅ) into ๐(๐ฅ):
๐(๐(๐ฅ)) = 5*log(5๐ฅ) + 4
So, the correct answer is A. (๐โ ๐)โข(๐ฅ)=5โข๐ฅlog(5โข๐ฅ)+4.
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