# Answer the following: Find the range of the following function. f(x) = x9+x2 - Mathematics and Statistics

Sum

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].

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 6 Functions
Miscellaneous Exercise 6 | Q II. (41) (b) | Page 132