Question

ℎ: ℝ → ℝ, ℎ() = sin + 3 , ∈ ℝ, then Range h is​

Answer 1

h is function defined as

$h:\mathbb{R}\to \mathbb{R}\\h(x)=\sin(x)+3$

We know that,

$-1\leq\sin(x)\leq 1\\\implies -1 + 3\leq\sin(x)+3\leq 1+3\\\implies -2\leq h(x)\leq4$

This means that the value of h is anywhere in $\left[-2,4\right]$

$\therefore Range\:of\:h,\mathcal{R}(h)=\left[-2,4\right]$