Question

plz solve it fully
its immediate ​

Answer 1

Answer:

Range [-1,-1/3]

Step-by-step explanation:

-1≤cos x≤1

0≤|cos x|≤1

0≤2|cos x|≤2

-3≤2|cos x|-3≤-1

-1/3≥1/(2|cos x|-3)≥-1

Answer 2

Answer:

Range = [-1 , -1/3 ]

Step-by-step explanation:

We know that range of cos x function is [-1, 1].

So,

=> 0 ≤ | cos x | ≤ 1

Multiply the inequality with 2

=> 0 ≤ 2 | cos x | ≤ 2

Subtract 3 from the inequality

=> -3 ≤ 2 | cos x | - 3 ≤ 2 - 3

=> -3 ≤ 2 | cos x | - 3 ≤ -1

By reciprocating the inequality, sign of inequality will be reversed.

=> -1/3 ≥ 1/ ( | cos x | -3 ) ≥ -1

So the function f(x) = 1/( | cos x | -3) will always lies between the intervals [- 1, -1/3 ]

So the range of the given function is [-1, -1/3 ]