Question

explain why the graphs of y=csc x and y=-ksinx will never intersect for any positive value of k

Answer 1

@mml I think I can explain it, just give me a minute please.

Answer 2

y = csc(x) and y = -ksin(x) will intersect when
csc(x) = -ksin(x)
1/sin(x) = - ksin(x)
1 = -ksin^2(x)
sin^2(x) = -1/k
The lefty hand side is always positive or zero.
If k is positive, the right hand side will be negative and there will be no real solution.

Answer 3

thanks

Answer 4

you are welcome.

Answer 5

can you also explain what the Inverse Compotistion Rule is?

Answer 6

If f(x) is a function and g(x) is its inverse function then:
f(g(x)) = x

Answer 7

The function f takes x and transforms it into f(x)
The inverse function g takes f(x) and transforms it back to x.

Or, the function g takes x and transforms it to g(x)
The function f takes g(x) and transforms it back to x (that is, f(g(x)) = x).