Find the domain and range of the function f(x)=1+x2x2

f(x)=1+x2x2 domain is Rlet y=1+x2x2⇒y+x2y=x2x2(y−1)+y=0x2=1−yy⇒x=±1−yy, y=1 & y≯1so range is [0,1)

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Find the domain and range of the function f ( x ) = { x ^ { 2

Question

Find the domain and range of the function $f (x) = \frac{x ^{2}}{1 + x ^{2}}$

R^{+}

and

R

R

and

[0, 1)

[2, 5]

and

[0, 1)

(2, 5)

and

(3, 5)

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Alexander Discussed

Find the domain and range of the function

f (x) = \frac{x ^{2}}{1 + x ^{2}}

9 mins ago

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9 mins ago

f (x) = \frac{x ^{2}}{1 + x ^{2}}

domain is R

let

y = \frac{x ^{2}}{1 + x ^{2}} \Rightarrow y + x^{2} y = x^{2}

x^{2} (y - 1) + y = 0

x^{2} = \frac{y}{1 - y} \Rightarrow x = \pm \frac{y}{1 - y},

y \neq = 1

y ≯ 1

so range is

[0, 1)

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Question Text	Find the domain and range of the function $f (x) = \frac{x ^{2}}{1 + x ^{2}}$
Answer Type	Text solution:1
Upvotes	150