I have the following theorem "If the function g is continuous everywhere and the function f is continuous everywhere, then the composition of f o g is continuous everywhere."
How can I directly apply this theorem to show that the equations
1) sin(x^3+7x+1)
2) |sinx|
3) cos^3 (x+1)
are continuous everywhere?
+128408 Note that f o g means we are putting g into f
1) Let f = sin x ....... a sinusoidal function is continuous everywhere
Let g = x^3 + 7x + 1......this is a polynomial....so it is continuous everywhere
So f o g = sin (x^3 + 7x + 1) is continuous
2) Let f = lx l .......the basic absolute value function is contimuous everywhere
Let g = sin x (continuous everywhere )
So f o g = l sin x l is continuous
3) As before
f = cos ^3 x sinusoidal function { continuous everywhere }
g = x +1 linear function {continuous everywhere}
So
f o g = cos^3 ( x + 1) is continuous
