which of the following function(s) is/are Transcendental?

f (x) = 5 sin \sqrt{x}

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f (x) = \frac{2 sin 3 x}{x^{2} + 2 x - 1}

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f (x) = \sqrt{x^{2} + 2 x - 1}

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f (x) = (x^{2} + 3) 2^{x}

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Solution

The correct options are
A $f (x) = 5 sin \sqrt{x}$
B $f (x) = \frac{2 sin 3 x}{x^{2} + 2 x - 1}$
D $f (x) = (x^{2} + 3) 2^{x}$
Functions of following category are transcendental functions.
$f (x) = x^{π}$
$f (x) = c^{x}, c \neq 0, 1$
$f (x) = x^{x}$
$f (x) = x^{\frac{1}{x}}$
$f (x) = l o g_{c} x, c \neq 0, 1$
$f (x) = s i n (x)$
Option A,B,D fall in the following category of functions. Hence they are transcendental.

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Similar questions

Q. Which of the following functions from Z to Z are bijections?
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(b) f(x) = x + 2
(c) f(x) = 2x + 1
(d) f(x) = x² + 1

Q. Which of the following functions form Z to itself are bijections?
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f (x) = x^{3}

(b)

f (x) = x + 2

(c)

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(d)

f (x) = x^{2} + x

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(ii) $f (x) = \frac{1}{x - 7}$
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(iv) $f (x) = \frac{2 x + 1}{x^{2} - 9}$
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How many of the following pairs of function are identcal

(a) f (x) = $\frac{x^{2}}{x}, g (x) = x$

(b) f(x) = $\frac{x^{2} - 1}{x - 1}$ g(x) = x + 1

(d) $f (x) = \frac{x}{x^{2}}, g (x) = \frac{1}{x}$

How many of the following pairs of function are identcal

(a) $f (x) = \frac{x^{2}}{x}, g (x) = x$

(b) $f (x) = \frac{x^{2} - 1}{x - 1}, g (x) = x + 1$

(d) $f (x) = \frac{x}{x^{2}}, g (x) = \frac{1}{x}$

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which of the following function(s) is/are Transcendental?

The correct options are A f(x)=5sin√x B f(x)=2sin3xx2+2x−1 D f(x)=(x2+3)2xFunctions of following category are transcendental functions.f(x)=xπf(x)=cx,c≠0,1f(x)=xxf(x)=x1xf(x)=logcx,c≠0,1f(x)=sin(x)Option A,B,D fall in the following category of functions. Hence they are transcendental.