Question

Given that F(x) = cos2(x + 9), find functions f,g and h such that F = fogoh

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.