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Questions and Answers
The inverse function of f(x) = 2x+3 is f-1(x) = (x-3)/2.
The inverse function of f(x) = 2x+3 is f-1(x) = (x-3)/2.
True (A)
The inverse function undoes the original function and returns the original value.
The inverse function undoes the original function and returns the original value.
True (A)
The inverse function of f(x) = 2x+3 is f-1(y) = (y-3)/2.
The inverse function of f(x) = 2x+3 is f-1(y) = (y-3)/2.
True (A)
When the function f turns the apple into a banana, the inverse function f-1 turns the banana back to the apple.
When the function f turns the apple into a banana, the inverse function f-1 turns the banana back to the apple.
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The inverse function is usually denoted by adding a little '-1' after the function name.
The inverse function is usually denoted by adding a little '-1' after the function name.
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Study Notes
Properties of Inverse Functions
- The inverse function reverses the operation of the original function, returning the original value.
- If f(x) = 2x+3, then its inverse function f-1(x) = (x-3)/2.
- The inverse function of f(x) = 2x+3 can also be denoted as f-1(y) = (y-3)/2, using a different variable y instead of x.
Analogy for Inverse Functions
- The inverse function can be thought of as "reversing" the operation of the original function, similar to how turning an apple into a banana can be reversed to turn the banana back into an apple.
Notation for Inverse Functions
- Inverse functions are typically denoted by adding a small '-1' to the original function name, such as f-1(x) or f-1(y).
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