Find the range of values for the function y = 9-2 * cos6x.

The cosine of a number can take values from -1 to 1, inclusive. therefore

-1 <= cos6x <= 1.

We multiply all the terms of the inequality by -2 (in this case, the signs are reversed):

-2 * (-1)> = -2 * cos6x> = -2 * 1;

2> = -2 * cos6x> = -2.

We rewrite this double inequality as follows:

-2 <= -2 * cos6x <= 2.

Add to all the terms of inequality 9:

9 – 2 <= 9 – 2 * cos6x <= 9 + 2;

7 <= 9 – 2 * cos6x <= 11.

Thus, the expression 9 – 2 * cos6x can take any values lying in the range from -7 to 11, including the boundary points -7 and 11.