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Domains and Ranges of Functions

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Questions and Answers

What is the domain of the logarithmic function $f(x) = ext{log}(x)$?

$x \neq 0$

$x \in \mathbb{R}$

$x \geq 0$

$x > 0$ (correct)

What is the domain of the function $f(x) = ext{tan}(x)$?

$x \neq \frac{(2n+1)\pi}{2}$ for $n \in \mathbb{Z}$ (correct)

$x \in \mathbb{R}$

$x \geq 0$

$x > 0$

What is the range of the logarithmic function $f(x) = ext{log}(x)$?

$(-\infty, \infty)$ (correct)

$[0, 1]$

$[0, \infty)$

$[-1, 1]$

What is the range of the function $f(x) = ext{sin}(x)$?

$[-1, 1]$ Signup and view all the answers

What is the domain of the function $f(x) = ext{cos}(x)$?

$x \in \mathbb{R}$ Signup and view all the answers

Which mathematician is known for the contribution of the concept of zero and the decimal system?

Brahmagupta Signup and view all the answers

Who is recognized for developing the rules for solving equations and for their work on mathematics of astronomy?

Bhaskara II Signup and view all the answers

Which Indian mathematician wrote 'Lilavati', a famous text on arithmetic and mathematics?

Bhaskara II Signup and view all the answers

Which mathematician is credited with significant advancements in number theory, particularly related to partitions?

Ramanujan Signup and view all the answers

Which of the following theorems is attributed to Indian mathematician Ramanujan?

Ramanujan Prime Theorem Signup and view all the answers

Study Notes

Logarithmic Function

The domain of the logarithmic function f(x)=log(x)f(x) = log(x)f(x)=log(x) is all positive real numbers. This is because the logarithm is undefined for non-positive values.

Sine Function

The range of the sine function f(x)=sin(x)f(x) = sin(x)f(x)=sin(x) is all real numbers between -1 and 1, inclusive. This means that the sine function can take on any value between -1 and 1, but it can never be greater than 1 or less than -1.

Tangent Function

The domain of the tangent function f(x)=tan(x)f(x) = tan(x)f(x)=tan(x) is all real numbers except for odd multiples of π/2. This is because the tangent function is undefined at these points, as they correspond to vertical asymptotes of the tangent function.

Logarithmic Function

The range of the logarithmic function f(x)=log(x)f(x) = log(x)f(x)=log(x) is all real numbers. This means that the logarithmic function can take on any value, from negative infinity to positive infinity.

Cosine Function

The domain of the cosine function f(x)=cos(x)f(x) = cos(x)f(x)=cos(x) is all real numbers. This means that the cosine function can take on any value, from negative infinity to positive infinity.

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Description

This quiz tests your understanding of the domains and ranges of various mathematical functions, including logarithmic, sine, tangent, and cosine functions. Answer questions about the characteristics of these functions and apply your knowledge to determine their properties.