JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

A function

y=f(x)

has a second order derivatives

f^{\prime \prime}(x)=6(x-1)

. If its graph passes through the point

(2,1)

and at that point the tangent to the graph is

y=3 x-5

, then the function is

View answer and explanation

Correct option: B

(x-1)^3

Option B (

(x-1)^3

) is correct because it satisfies the given second derivative, passes through the point (2,1), and has the tangent y=3x-5 at that point.

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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\}