Let f be the function from R to R defined by f(x) = x^{2}. Find

Harlen Pritchard

Harlen Pritchard

Answered question

2021-09-22

Let f be the function from R to R defined by f(x)=x2. Find
f1(x0<x<1)

Answer & Explanation

pattererX

pattererX

Skilled2021-09-23Added 95 answers

Given: f:RR
f(x)=x2
f1({x|0<x<1}) contains all R  elements with a real integer between 0 and 1 as their image.
0<f(x)<1
Since f(x)=x2
0<x2<1
The square x2 is less than 1 if x is between -1 and 1.
The square x2 is more than 0, when x is not equal to 0.
(1<x<1)(x 0)
f1({x|0<x<1}) thus contains all real numbers between -1 and 1, except for 0.
f1({x|0<x<1})={x|(1<x<1)(x0)}
Or equivalently: f1({x|0<x<1})={x|(1<x<0)(0<x<1)}

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