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Questions and Answers
What is the inverse of function f given by $f = ig{(-2, 0), (0, 1), (2, 3), (3, 4)ig}$?
What is the inverse of function f given by $f = ig{(-2, 0), (0, 1), (2, 3), (3, 4)ig}$?
- $f^{-1} = ig\{(0, -2), (1, 0), (2, 3), (3, 4)ig\}$
- $f^{-1} = ig\{(-2, 0), (0, 1), (3, 2), (4, 3)ig\}$
- $f^{-1} = ig\{(-2, 0), (1, 0), (2, 3), (4, 3)ig\}$
- $f^{-1} = ig\{(0, -2), (1, 0), (3, 2), (4, 3)ig\}$ (correct)
What is the domain and range of the inverse of function f?
What is the domain and range of the inverse of function f?
- Domain: $(0, 1, 3, 4)$, Range: $(0, 1, 3, 4)$ (correct)
- Domain: $(-2, 0, 2, 3)$, Range: $(0, 1, 3, 4)$
- Domain: $(-2, 0, 2, 3)$, Range: $(-2, 0, 2, 3)$
- Domain: $(0, 1, 3, 4)$, Range: $(-2, 0, 2, 3)$
Evaluate $f(f^{-1}(1))$ for the given functions.
Evaluate $f(f^{-1}(1))$ for the given functions.
- $f(f^{-1}(1)) = 0$
- $f(f^{-1}(1)) = -2$
- $f(f^{-1}(1)) = 2$
- $f(f^{-1}(1)) = 1$ (correct)
What are the properties of the graph of function $f$ and its inverse $f^{-1}$?
What are the properties of the graph of function $f$ and its inverse $f^{-1}$?
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What is $f^{-1}(f(2))$ for the given functions?
What is $f^{-1}(f(2))$ for the given functions?
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Study Notes
Inverse of Function f
- The inverse of function f is denoted by f^(-1)
- f^(-1) is found by swapping the x and y values in the given points: f^(-1) = {(0, -2), (1, 0), (3, 2), (4, 3)}
Domain and Range of Inverse of Function f
- Domain of f^(-1) is the range of f: {-2, 0, 2, 3}
- Range of f^(-1) is the domain of f: {0, 1, 3, 4}
Evaluating f(f^(-1)(1))
- To evaluate f(f^(-1)(1)), first find f^(-1)(1) = 0
- Then, f(f^(-1)(1)) = f(0) = 1
Properties of Graph of Function f and its Inverse f^(-1)
- The graphs of f and f^(-1) are reflections of each other over the line y = x
- The domain of f is the range of f^(-1) and vice versa
- The range of f is the domain of f^(-1) and vice versa
Evaluating f^(-1)(f(2))
- To evaluate f^(-1)(f(2)), first find f(2) = 3
- Then, f^(-1)(f(2)) = f^(-1)(3) = 2
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