Select the correct answer.What is the inverse of function f?๐โก(๐ฅ)=๐ฅ+7 A. ๐-1โก(๐ฅ)=(๐ฅ+7)2,for๐ฅโฅ-7 B. ๐-1โก(๐ฅ)=๐ฅ2+7,for๐ฅโฅ-7 C. ๐-1โก(๐ฅ)=๐ฅ2โ7,for๐ฅโฅ7 D. ๐-1โก(๐ฅ)=(๐ฅโ7)2,for๐ฅโฅ7
Question
Select the correct answer.What is the inverse of function f?๐โก(๐ฅ)=๐ฅ+7 A. ๐-1โก(๐ฅ)=(๐ฅ+7)2,for๐ฅโฅ-7 B. ๐-1โก(๐ฅ)=๐ฅ2+7,for๐ฅโฅ-7 C. ๐-1โก(๐ฅ)=๐ฅ2โ7,for๐ฅโฅ7 D. ๐-1โก(๐ฅ)=(๐ฅโ7)2,for๐ฅโฅ7
Solution
The inverse of a function essentially "undoes" the operation of the original function. In this case, the original function is f(x) = x + 7. To find the inverse, we need to swap x and y and solve for y:
Step 1: Swap x and y. This gives us x = y + 7. Step 2: Solve for y. This gives us y = x - 7.
So, the inverse of the function f(x) = x + 7 is f^-1(x) = x - 7. However, this option is not given in the choices. There seems to be a mistake in the options provided as none of them are the correct inverse of the given function.
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