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Question
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
Solution
f(x) = `x/(9 + x^2)`
Let y = f(x)
∴ y = `x/(9 + x^2)`
∴ yx2 + 9y = x
∴ yx2 – x + 9y = 0
This is a quadratic equation in x
∵ x is real
∴ Δ ≥ 0
∴ ( – 1)2 – 4(y)(9y) ≥ 0
∴ 1 – 36y2 ≥ 0
∴ 36y2 ≤ 1
∴ `y^2 ≤ 1/36`
∴ `-1/6 ≤ y ≤ 1/6`
∴ Range = `[-1/6, 1/6]`.
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