Question

Find the domain and range of the following function: f(x)=5+4cosx ​

Answer 1

Step-by-step explanation:

We have,

$\tt{f(x) = 5 + 4cos(x)}$

$\sf{ Since \: \: \blue{cos(x)} \: \: is \: defined \: \: for \: \: all \: \: \blue{x \in \mathbb{ R } }}$

So,

$\rm{ \pink{dom(f) \in \mathbb{ R} }}$

Now,

We know,

$\sf{ - 1\leqslant cos(x) \leqslant 1}$

$\sf{ \implies - 4\leqslant 4cos(x) \leqslant 4}$

$\sf{ \implies 1\leqslant 5 + 4cos(x) \leqslant 9}$

So,

$\rm{ \pink{dom(f) \in [1 , 9] }}$