JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}(\mathrm{x}-\mathrm{p})}{\mathrm{q}-\mathrm{p}}+\frac{\mathrm{x}(\mathrm{x}-\mathrm{q})}{\mathrm{p}-\mathrm{q}}, \mathrm{p} \neq \mathrm{q}

. What is the value of

f(p)+f(q)

View answer and explanation

Correct option: B

\mathrm{f}(\mathrm{p}+\mathrm{q})

Option B (

f(p+q)

) is correct because by substituting p and q into the function, we find that f(p) = p and f(q) = q, and then f(p+q) simplifies to p+q, which is equal to f(p) + f(q).

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