Question

If f(x) = Sin3x+x , verify that f(-x)=-f(x).

Answer 1

True

Explanation:

Given a function:

`\displaystyle{f(x)=\sin 3x + x}`

Verify that f(-x) = -f(x) by substitution -- therefore:

`\displaystyle{f(-x) = -f(x)}\\\\\displaystyle{\sin 3\left(-x\right)+\left(-x\right) = -\left(\sin 3x + x\right)}\\\\\displaystyle{\sin \left(-3x\right) - x = -\sin 3x - x}\\\\\displaystyle{-\sin 3x - x = -\sin 3x - x}`

Both sides are equal, hence f(-x) = -f(x).