Chapter 4.1, Problem 8QR

To determine

To solve: The given function as the composite function of two or more of f,g and h .

Answer to Problem 8QR

The given function as a composite function is $h(g(f(x)))$ .

Explanation of Solution

Given information: $f(x)=\cos x,g(x)=\sqrt{x+2},h(x)=3x^2$

Calculation:

  $\begin{array}{c}3\cos x+6=3(\cos x+2)\\ $ =3({(\sqrt{\cos x+2})}^2)\mathrm{....}(1)$\end{array}$

Now, from the given information equation (1) will become,

  $\begin{array}{l}$ =3({(\sqrt{f(x)+2})}^2)$$ =3(g{(f(x))}^2)$=h(g(f(x)))\end{array}$