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Sum

Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.

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#### Solution

f(x) =`("x - 2")/("x + 1")`, x ≠ 0

For function to be increasing, f '(x) > 0

Then f '(x) = `(("x + 1") "d"/"dx" ("x - 2") - ("x - 2") "d"/"dx" ("x" + 1))/("x + 1")^2`

`= (("x + 1") - ("x - 2"))/("x + 1")^2 = ("x" + 1 - "x" + 2)/("x" + 1)^2`

`= 3/("x + 1")^2` > 0 ....[∵ (x + 1) ≠ 0, (x + 1)^{2} > 0]

Thus, f(x) is an increasing function for x ≠ - 1.

Concept: Increasing and Decreasing Functions

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