JEE Main 2026 · 4 Apr · Shift 2 · Mathematics Q1

MathematicsSingle correct+4 / -1Question 1 of 75

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

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

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

only (I) is TRUE

only (II) is TRUE

both (I) and (II) are TRUE

neither (I) nor (II) is TRUE

Answer and worked solution

Official answer: A

(I) For an increasing $f$ , $f(x)=f^{-1}(x)$ exactly when $f(x)=x$ : $(x-1)^4=x-1$ gives $x=1,2$ . Two elements: true.

(II) $f(x)=f^{-1}(x+1)$ means $f(f(x))=x+1$ . Let $h(x)=f(f(x))-x-1$ .

So $h$ has a root and the set is not empty: false.

(A)

Topics:Composition and inverse functions

JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 1