Question

The function f(x)-->4-3sinx is defined for the domain 0≤x≤2pi

Find the set of values of k for which the equation f(x)=k has no solution

Answer 1

f(x)=k has no solution for values of k greater than 7 and less than 1.

Answer 2

Take h(x) = sin(x), you know how his graph looks. You can easily consider that h(x) = k for -1≤k≤1. Now take j(x) = -3sin(x). This is just h(x), but now three times higher and lower, and upside down. Therefore, j(x) = k for -3≤k≤3. If you now take f(x), you see f(x) is actually just j(x), but then 4 higher. Therefore, f(x) = k has solutions for 1≤k≤7.

Answer 3

I don't understand the explanation...

Answer 4

Oh, I understand now :)

Answer 5

But f(x)=k does have a solution for k=1 and for k=7.
The answer is the set of real numbers excluding numbers greater than 1 and less than 7.

Answer 6

That's exactly what I said.
"Therefore, f(x) = k has solutions for 1≤k≤7."
Therefore, f(x) = k has NO solutions for k < 1 and k > 7.

Answer 7

Sorry, I should have read you reply more carefully:(