Question

If f(x) = [x] and g(x) = cos($\pi$x), then the range of gof is.

• A. {0}
• B. {-1, 1}
• C. {1, 0, 1}
• D. [1, 1]

Answer 1

The correct option is B {-1, 1}

$gof=g\left(f\right(x\left)\right)=\cos \left(\pi f\right(x\left)\right)=\cos \left(\pi \right[x\left]\right)=\cos ($ integral multiple of $\pi )=-1$ or $1$
Hence range of $gof$ is $\{-1,1\}$