Which of the following function(s) is/are tra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) function is called transcendental if it is not algebraic. Algebraic functions are those that can be expressed as the root of a polynomial equation

Vedclass · Accepted Answer

All of the above

Vedclass · Answer

(D) function is called transcendental if it is not algebraic. Algebraic functions are those that can be expressed as the root of a polynomial equation with polynomial coefficients. Functions involving trigonometric,exponential,or logarithmic terms are generally transcendental. In option $A$,$f(x) = 5 \sin \sqrt{x}$ involves a trigonometric function. In option $B$,$f(x) = \frac{2 \sin 3x}{x^2 + 2x - 1}$ involves a trigonometric function. In option $C$,$f(x) = (x^2 + 3) \cdot 2^x$ involves an exponential function. Since all these functions are non-algebraic,they are all transcendental functions. Therefore,the correct option is $D$.

Which of the following function$(s)$ is/are transcendental?

Similar Questions

Let $Z$ denote the set of integers. Define $f: Z \rightarrow Z$ by $f(x) = \begin{cases} \frac{x}{2}, & x \text{ is even} \\ 0, & x \text{ is odd} \end{cases}$. Then $f$ is:

If $f: Z \rightarrow Z$ is defined by $f(x)=\begin{cases} \frac{x}{2}, & \text{if } x \text{ is even} \\ 0, & \text{if } x \text{ is odd} \end{cases}$,then $f$ is

The function $f:R \to R$ defined by $f(x) = e^x$ is

Prove that the Greatest Integer Function $f: R \rightarrow R$,given by $f(x)=[x]$,is neither one-one nor onto,where $[x]$ denotes the greatest integer less than or equal to $x$.

If $f: N \times N \rightarrow N$ defined by $f(m, n) = mn$,then $f$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module