# Test whether the function is increasing or decreasing. f(x) = x-1x, x ∈ R, x ≠ 0, - Mathematics and Statistics

Sum

Test whether the function is increasing or decreasing.

f(x) = "x" -1/"x", x ∈ R, x ≠ 0,

#### Solution

f(x) = "x" - 1/"x", "x" in "R"

therefore "f"'("x") = 1 - (- 1/"x"^2) = 1 + 1/"x"^2

∵ "x" ne 0, for all values of x, "x"^2>0

therefore 1/"x"^2 > 0, 1 + 1/"x"^2 is always positive

thus f'(x)>o , for all x ∈ R

Hence f(x) is increasing function.

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Exercise 4.2 | Q 1.2 | Page 106