Find the range (1) y = cos & sup2; x-4sinx + 1

Find the range (1) y = cos & sup2; x-4sinx + 1

sin²x+cos²x=1
y=(1-sin²x)-4sinx+1
=-sin²x-4sinx+2
=-(sinx-2)²+6
-1

The range of the function FX = 4 / (X-2), (x belongs to [3,6]) is?

If x belongs to [3,6], then X-2 belongs to [1,4], then 1 / (X-2) belongs to [1 / 4,1]
Then the range of this function is [1,4]

Given the function f (x) = ax + 3 / X-1, if (2,7) is a point on the f ^ - 1 (x) image, find the range of y = f (x)

F (x) = ax + 3 / X-1, if (2,7) is a point on f ^ - 1 (x) image
So the point on f (x) has (7,2)
So f (7) = (7a + 3) / (7-1) = 2
7a+3=12
a=9/7
So f (x) = (9x + 21) / (7x-7) = 9 / 7 + 30 / (7x-7)
So the range is (- ∞, 9 / 7) U (9 / 7, + ∞)