For the function f:[1, ∞) →[1, ∞) defined by f(x)=(x-1)^4+1, among the two statements: (I) The set S ={x ∈[1, ∞): f(x)=f^-1(x)} contains exactly two elements, and (II) The set S ={x ∈[1, ∞): f(x)=f^-1(x+1)} is an empty set,

For the function f:[1, ∞) →[1, ∞) defined by f(x)=(x-1)^4+1, among the two statements:…

Mathematics · 2026

JEE Main · 4 April 2026, Shift 2 · Q1

For the function $\displaystyle f:[1, \infty) \rightarrow[1, \infty)$ defined by $\displaystyle f(x)=(x-1)^4+1$, among the two statements:

(I)

The set $\displaystyle \mathrm{S}=\left\{x \in[1, \infty): f(x)=f^{-1}(x)\right\}$ contains exactly two elements, and

(II)

The set $\displaystyle \mathrm{S}=\left\{x \in[1, \infty): f(x)=f^{-1}(x+1)\right\}$ is an empty set,