Question

find the range of
y=x2/1+x2

pls guys fast

from calculus

Answer 1

wer:

(−∞,−1)∪[0,∞)

Explanation:

Given:

f(x)=x21−x2

Let y=f(x) and attempt to solve for x...

y=f(x)=x21−x2=1−(1−x2)1−x2=11−x2−1

Add 1 to both ends to get:

y+1=11−x2

Multiply both sides by 1−x2y+1 to get:

1−x2=1y+1

Add x2−1y+1 to both sides to get:

1−1y+1=x2

In order for this to have a real valued solution, we require:

1−1y+1≥0

That is:

yy+1≥0

Hence we require one of:

(y≥0∧y+1>0)→y∈[0,∞)

(y<0∧y+1<0)→y∈(−∞,−1)

So the range of f(x) is (−∞,−1)∪[0,∞)

graph{x^2/(1-x^2) [-10, 10, -5, 5]}

Answer 2

$\huge{hey}$


$\huge{ \mathfrak{here \: is \: answer}}$


$\bf{see \: in \: pic}$
$\huge \boxed{ \ulcorner{hope \: it \: helps}}$


$\huge{ \mathbb{THANKS}}$