JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

Let

f\left( x \right) = \left| {\begin{array}{cccccccccccccccccccc} a&{ - 1}&0 \\ {ax}&a&{ - 1} \\ {a{x^2}}&{ax}&a \end{array}} \right|,\,a \in R.

Then the sum of the square of all the values of

a,

for which

2f'\left( {10} \right) - f'\left( 5 \right) + 100 = 0,

View answer and explanation

Correct option: C

125

The correct answer is C (125) because it is the sum of the squares of all values of a that satisfy the given condition involving the derivative of the determinant.

More Questions from FUNCTIONS

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

, where

f(x)=x(4-x)

, then

f^{-1}(x)

is given by: If

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

and

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

, then Let

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

be defined by

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

, then

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

equals Let

f: R \rightarrow R

be defined as

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

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

. Then the set

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

contains