What is the domain and range of $cos (\frac{1}{x})$ $cos(1/x)$ ?

Question

12437 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-28T04:53:33

Domain: $(- \infty, 0) \cup (0, + \infty)$ $(-oo,0)uu(0,+oo)$ Range: $[- 1, + 1]$ $[-1,+1]$

$f (x) = cos (\frac{1}{x})$ $f(x) = cos(1/x)$

f(x) is defined $forall x in RR: x!=0$

Hence, the domain of $f(x)$ is $(-oo,0)uu(0,+oo)$

Consider, $-1<=f(x)<= +1 forall x in RR: x!=0$

And, $lim_(x->-oo) f(x) =1$

And, $lim_(x->+oo) f(x) =1$

Also, $lim_(x->0) f(x)$ does not exist.

Hence, the range of $f(x)$ is $[-1,+1]$

We may deduce these results from the graph of $fx)$ below.

graph{cos(1/x) [-3.464, 3.465, -1.734, 1.728]}

What is the domain and range of cos(1/x)cos(1x)cos(1/x)?