Functions in Mathematics

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What is the mathematical definition of a function?

$y = x^2$

$y = f(x)$ (correct)

$f: X \rightarrow Y$

$x = f^{-1}(y)$

Which type of function is characterized by $f(-x) = f(x)$?

Increasing Function

Periodic Function

Even Function (correct)

Odd Function

What is the condition for a function to be considered decreasing?

$f(x_1) = f(x_2)$ if $x_1 \neq x_2$

$f(x_1) > f(x_2)$ if $x_1 < x_2$

$f(x_1) < f(x_2)$ if $x_1 > x_2$ (correct)

$f(x + 2T) = f(x)$

What does the notation $f: R \rightarrow R$ indicate about a function?

It is a Real-valued Function Signup and view all the answers

What characterizes the inverse function of $f: X \rightarrow Y$?

$x = f^{-1}(y)$ Signup and view all the answers

What characterizes the inverse function of $f: X \rightarrow Y$?

It is one-to-one and written as $x = f^{-1}(y)$ Signup and view all the answers

Which type of function is characterized by $f(x + 2T) = f(x)$?

Periodic Function Signup and view all the answers

What characterizes the constant function?

$f(x_1) = f(x_2)$ for all $x_1, x_2$ in the domain Signup and view all the answers

What is the condition for a function to be considered decreasing?

$f(x_1) > f(x_2)$ if $x_1 < x_2$ Signup and view all the answers

Which type of function is characterized by $f(-x) = -f(x)$?

Odd Function Signup and view all the answers

Functions in Mathematics

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Questions and Answers

What is the mathematical definition of a function?

Which type of function is characterized by $f(-x) = f(x)$?

What is the condition for a function to be considered decreasing?

What does the notation $f: R \rightarrow R$ indicate about a function?

What characterizes the inverse function of $f: X \rightarrow Y$?

What characterizes the inverse function of $f: X \rightarrow Y$?

Which type of function is characterized by $f(x + 2T) = f(x)$?

What characterizes the constant function?

What is the condition for a function to be considered decreasing?

Which type of function is characterized by $f(-x) = -f(x)$?

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