Math Problem Statement
Y=2x+1/x-5 fungsi invers y (y-1)
Solution
To find the inverse function of , we proceed with the following steps:
Step 1: Rewrite the Function
The function given is:
To find the inverse, we’ll first replace with and with :
Step 2: Solve for in Terms of
Now, we want to isolate on one side of the equation.
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Start by multiplying both sides by to get rid of the denominator:
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Distribute on the left side:
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Move terms involving to one side and constants to the other:
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Factor out from the left side:
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Finally, solve for by dividing both sides by :
Conclusion
The inverse function of is:
Would you like additional details or have any questions?
Here are some related questions to consider:
- How can we verify if two functions are inverses of each other?
- What is the domain and range of the inverse function ?
- How does the process change if we have a different type of function, such as a quadratic?
- What applications in real life involve finding inverse functions?
- How do we handle inverse functions for functions that are not one-to-one?
Tip: Always check that the function is one-to-one before attempting to find its inverse; this ensures that an inverse function exists.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Inverse Functions
Formulas
y = (2x + 1) / (x - 5)
Inverse function: y = (5x + 1) / (x - 2)
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 10-12