Question Type 2: Finding parameter values such that a function is odd or even or neither Exercises

Determine $k$ such that $f(x)=\sin(x)+k\cos(x)$ is odd.

Determine the conditions on $a,b,c,d$ so that $f(x)=ax^3+bx^2+cx+d$ is an odd function.

Find all real $a$ for which $f(x)=\arccos(\sin(ax))$ is an odd function.

Determine all real $a$ such that $f(x)=\arccos\bigl(\sin(\tan(ax))\bigr)$ is odd.

Find the value of $k$ such that the function $f(x)=x^2+kx$ is even.

Determine whether $f(x)=\cos(\sin(x))$ is even, odd, or neither.

For which real $a$ is $f(x)=\sin(ax)$ an even function?

Find $k$ so that $f(x)=x^4+kx$ is even.

Decide whether the function $f(x)=\sin(x)+\cos(x)$ is even, odd, or neither.

Find all real $a$ for which $f(x)=\arccos\bigl(\sin(ax)\bigr)$ is an even function.

Find the value of $k$ such that $f(x)=k\sin(x)+\cos(2x)$ is an even function.

Determine all real $a$ such that $f(x)=\arccos\bigl(\sin(\tan(ax))\bigr)$ is even.