Question

find the domain and range of the function f(x) =-1×1​

Answer 1

Answer



Narad T.

Apr 6, 2018

The domain is x∈R. The range is y∈(0,1]

Explanation:

The denominator is =1+x2

∀x∈R, 1+x2>0

Therefore,

The domain of f(x) is x∈R

To determine the range, proceed as follows

y=11+x2

y(1+x2)=1

y+yx2=1

yx2=1−y

x2=1−yy

x=√1−yy

The range of f(x) is the domain of x

(1−yy)>0

y∈R*+

1−y≥0

y≤1

Therefore,

The range is y∈(0,1]

graph{1/(1+x^2) [-11.25, 11.25, -5.625, 5.625]}