Question

given F(x)=cos^2(x+9) find functions f,g,h such that F=fogoh(x).

Answer 1

Answer:

The functions f(x), g(x) and h(x) such that F(x) = f\,\circ\,g\,\circ \,h (x) are f(x) = x^{2}, g(x) = \cos x and h(x) = x+9, respectively.

Step-by-step explanation:

Let F(x) = \cos ^{2}(x+9), if F(x) = f\,\circ\,g\,\circ \,h (x), then we derive f(x), g(x) and h(x) by using the following approach:

1) F(x) = \cos ^{2} (x+9) Given

2) f\,\circ\,g(x) =  \cos^{2} x  Definition of function composition/h(x) = x+9

3) f(x) = x^{2} Definition of function composition/g(x) = \cos x

4) f(x) = x^{2}, g(x) = \cos x, h(x) = x+9 From 2) and 3)/Result

The functions f(x), g(x) and h(x) such that F(x) = f\,\circ\,g\,\circ \,h (x) are f(x) = x^{2}, g(x) = \cos x and h(x) = x+9, respectively.