Question

Write the range of the function : y = x/1+x^2​

Answer 1

Answer:

Here, f(x)= x/x^2+1

thus, Domain(f) =R

Now, let y= f(x)

=>y=x/x2+1

=>y+yx2−x=0

=>yx2−x+y=0

then check whether the discriminant giving positive or negative value.

Here, we’ll get a real value of discriminant.

thus, 1−4y2≥0

=>4y2−1≤0

=>y2−1/4≤0

=>(y-1/2) (y+1/0) ≤0

=>-1/2 ≤y≤0

=> y ∈ [−1/2,1/2] - {0}

Hence, range= [−1/2,1/2]

Step-by-step explanation:

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