Let f:[0,3] → A be defined by f(x)=2x³-15x²+36x+7 and g:[0, ∞) → B be defined by g(x)=(x²⁰⁰)/(x²⁰⁰⁵+1). If both the functions are onto and S= Z: x A or x B, then n(S) is equal to:

Sets, Relations and Functions: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q84

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

Let

f:[0,3] \rightarrow A

be defined by

f(x)=2x^3-15x^2+36x+7

and

g:[0, \infty) \rightarrow B

be defined by

g(x)=\frac{x^{200}}{x^{2005}+1}

. If both the functions are onto and

S=\{x \in \mathbb{Z} : x \in A \text{ or } x \in B\}

, then

n(S)

is equal to:

JEE Main 2025 · January, Unspecified (session-level dataset) · Q84

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

Let

f:[0,3] \rightarrow A

be defined by

f(x)=2x^3-15x^2+36x+7

and

g:[0, \infty) \rightarrow B

be defined by

g(x)=\frac{x^{200}}{x^{2005}+1}

. If both the functions are onto and

S=\{x \in \mathbb{Z} : x \in A \text{ or } x \in B\}

, then

n(S)

is equal to: