Maharashtra State BoardHSC Arts 11th
Advertisement Remove all ads

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

Sum

Answer the following:

Find the range of the following function.

f(x) = `x/(9 + x^2)`

Advertisement Remove all ads

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?
Advertisement Remove all ads

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
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×