JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

Let

f:N \to R

be a function such that

f(x + y) = 2f(x)f(y)

for natural numbers

x

and

y

. If

f(1) = 2,\,

then the value of

\alpha

for which

\sum\limits_{k = 1}^{10} {f(\alpha + k)} = \frac{{512}}{3}({2^{20}} - 1)

holds, is:

View answer and explanation

Correct option: C

Option C (4) is correct because by substituting the function

f(x)

and simplifying the summation, we can find the value of

\alpha

to be 4.

More Questions from FUNCTIONS

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

f(x)=x(4-x)

f^{-1}(x)

g(f(x))=|\sin x|

f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

S=\left\{x: f(x)=f^{-1}(x)\right\}