The correct option is B f−1(x)=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩x,x<1√x,1≤x≤16x264,x>16
It can be inferred from the options that f is a bijective function.
Given f(x)=⎧⎨⎩x,x<1x2,1≤x≤48√x,x>4
Let f(x)=y⇒x=f−1(y) ⋯(1)
∴x=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩y,y<1√y,1≤√y≤4y264,y264>4⇒f−1(y)=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩y,y<1√y,1≤y≤16y264,y>16∴f−1(x)=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩x,x<1√x,1≤x≤16x264,x>16