Math  /  Algebra

QuestionFor the following function, a) determine whether it is one-to-one; b) if it is one-to-one, find its inverse function. f(x)=x+5f(x)=x+5
Is the given function a one-to-one function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Yes, the function is one-to-one. The inverse function is f1(x)=\mathrm{f}^{-1}(\mathrm{x})= \square (Simplify your answer.) B. No, the the function is not one-to-one.

Studdy Solution
Since the function is one-to-one, we can find its inverse. To find the inverse, follow these steps:
1. Replace f(x) f(x) with y y : $ y = x + 5 \]
2. Swap x x and y y to find the inverse: $ x = y + 5 \]
3. Solve for y y : $ y = x - 5 \]
4. Replace y y with f1(x) f^{-1}(x) : $ f^{-1}(x) = x - 5 \]
The function is one-to-one. The inverse function is f1(x)=x5 f^{-1}(x) = x - 5 .

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