Pls find the domain and range of the function given in the pic Also draw its graph - Maths - Relations and Functions

Question

Pls find the domain and range of the function given in the pic Also
draw its graph

Neha Sethi · Accepted Answer

Dear student
We have, fx=1-x2⇒1-x2≥0    ∵fx⇒f(x)≥0⇒-1≤x≤1⇒x∈-1,1Domain of f:x∈-1,1Range of f Let y =fx then y=1-x2⇒y2=1-x2⇒x=1-y2Clearly , x will take real values if 1-y2≥0⇒y2-1≤0⇒y-1y+1≤0⇒-1≤y≤1⇒y∈-1,1Also y=1-x2≥0 for all x∈-1,1So , y∈0,1 for all x∈-1,1Hence Range of f=0,1
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_58381ca7b9aaf%20png"
style="width: 850px; height: 525px;">
Regards

Pls find the domain and range of the function given in the pic. Also draw its graph.