JEE MATHEMATICS MCQ: TRANSFORMATIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

f\left( x \right)

be a real valued function defined by

f\left( {x + \lambda } \right) = 1 + {\left[ {2 - 5f\left( x \right) + 10{{\left\{ {f\left( x \right)} \right\}}^2} - 10{{\left\{ {f\left( x \right)} \right\}}^3} + 5{{\left\{ {f\left( x \right)} \right\}}^4} - {{\left\{ {f\left( x \right)} \right\}}^5}} \right]^{1/5}}

for all real x and some positive constant

\lambda

, then

f\left( x \right)

View answer and explanation

Correct option: B

A periodic function with period

2\;\lambda

The correct answer is A (A periodic function with period

\lambda

) because the function repeats its values after an interval of

2\lambda

, making it periodic.

More Questions from TRANSFORMATIONS

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1 + \cos \,\,56^\circ + \cos \,\,58^\circ - \cos \,\,66^\circ = \lambda \cos \,\,28^\circ \,\,\cos \,\,29^\circ \,\,\sin \,\,33^\circ

\lambda =

\cos \,\,\frac{\pi }{{11}} + \cos \,\,\frac{{3\,\pi }}{{11}} + \cos \,\,\frac{{5\,\pi }}{{11}} + \cos \,\,\frac{{7\pi }}{{11}} + \cos \,\,\frac{{9\,\pi }}{{11}}

\;\cos \,\,x + \cos \,\,y + \cos \,\,\alpha = 0\;\,\mathrm{and}\,\sin x + \sin \,\,y + \sin \,\,\alpha = 0

\cot \left( {\frac{{x + y}}{2}} \right)\;

f\left( x \right) = \sin \left( {\frac{{2x + 3}}{{6\;\pi }}} \right),

0 < x,\mathrm{ }y < \pi

\cos x + \cos y - \cos (x + y) = \frac{3}{2}

\sin x + \cos y

\mathrm{\;sin}\,\,36^\circ \,\,\sin \,\,72^\circ \,\,\sin \,\,108^\circ \,\,\sin \,\,144^\circ \;