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Inverse Functions Quiz

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Questions and Answers

What is the inverse of function f given by $f = ig{(-2, 0), (0, 1), (2, 3), (3, 4)ig}$?

$f^{-1} = ig\{(0, -2), (1, 0), (2, 3), (3, 4)ig\}$

$f^{-1} = ig\{(-2, 0), (0, 1), (3, 2), (4, 3)ig\}$

$f^{-1} = ig\{(-2, 0), (1, 0), (2, 3), (4, 3)ig\}$

$f^{-1} = ig\{(0, -2), (1, 0), (3, 2), (4, 3)ig\}$ (correct)

What is the domain and range of the inverse of function f?

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.

$f(f^{-1}(1)) = 0$

$f(f^{-1}(1)) = -2$

$f(f^{-1}(1)) = 2$

$f(f^{-1}(1)) = 1$ (correct)

What are the properties of the graph of function $f$ and its inverse $f^{-1}$?

<p>They are reflections of each other over the line $y = x$</p> Signup and view all the answers

What is $f^{-1}(f(2))$ for the given functions?

<p>$f^{-1}(f(2)) = 2$</p> Signup and view all the answers

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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Description

Test your understanding of inverse functions with this quiz. Explore questions related to ordered pairs, linear, cubic root, square root, logarithmic, and exponential functions, along with detailed solutions. Practice algebraically and graphically checking answers using the properties of each function and its inverse. Strengthen your skills in solving inverse function problems step by step.