IB Mathematics Analysis and Approaches 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 $f(x)=a{x}^3+b{x}^2+cx+d$ 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 $f(x)=\arccos (\sin (\tan (ax)))$ 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 $f(x)=\arccos (\sin (ax))$ 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 $f(x)=\arccos (\sin (\tan (ax)))$ is even.