Remediation Inverse Functions

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•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an inverse function?
Back
An inverse function reverses the effect of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y back to x.
2.
FLASHCARD QUESTION
Front
How can you determine if two functions are inverses?
Back
Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.
3.
FLASHCARD QUESTION
Front
What is the graphical representation of inverse functions?
Back
Inverse functions are reflections of each other across the line y = x.
4.
FLASHCARD QUESTION
Front
What is the inverse of the function f(x) = 2x + 3?
Back
f⁻¹(x) = (x - 3)/2.
5.
FLASHCARD QUESTION
Front
What is the inverse of the function f(x) = x² (for x ≥ 0)?
Back
f⁻¹(x) = √x.
6.
FLASHCARD QUESTION
Front
What is the importance of the domain and range in inverse functions?
Back
The domain of the original function becomes the range of the inverse function and vice versa.
7.
FLASHCARD QUESTION
Front
How do you find the inverse of a function algebraically?
Back
1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).
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