Determine even or odd function f x = sin x + tgx-x ^ 3
| August 6, 2021 | education
The function is even if f (-x) = f (x).
The function is odd if f (-x) = – f (x).
Consider the function f (x) = sin x + tan x – x ^ 3:
f (-x) = sin (-x) + tg (-x) – (-x) ^ 3.
Let us simplify by trigonometric formulas:
sin (-x) = -sin x,
tg (-x) = – tg x.
(-x) ^ 3 = (-1) ^ 3 * x ^ 3 = – x ^ 3.
We get:
f (-x) = sin (-x) + tg (-x) – (-x) ^ 3 = -sin x – tan x + x ^ 3 = – (sin x + tan x – x ^ 3) = – f (x).
Because f (-x) = – f (x), then the function is odd.
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