Q26Multiple correct4 Marks6 Aug 2023Define a function f(x)={x2+1,x<1,x3,x≥1.f(x)=\begin{cases}x^2+1, & x<1,\\ x^3, & x\ge1.\end{cases}f(x)={x2+1,x3,x<1,x≥1. Which of the following options is/are true?Af(x)f(x)f(x) is invertible in its domain.Bf(x)f(x)f(x) is invertible when the domain is restricted to [1,∞)[1,\infty)[1,∞).Cf(x)f(x)f(x) is invertible when the domain is restricted to [−1,1][-1,1][−1,1].DThe inverse of f(x)f(x)f(x) when the domain is restricted to [1,∞)[1,\infty)[1,∞) is f−1(x)=x1/3f^{-1}(x)=x^{1/3}f−1(x)=x1/3.EThe inverse of f(x)f(x)f(x) when the domain is restricted to (−∞,0)(-\infty,0)(−∞,0) is f−1(x)=x−1f^{-1}(x)=\sqrt{x-1}f−1(x)=x−1.
