# Math Help - f o g functions

1. ## f o g functions

Express the function in the form f g. (Use only elementary functions, but not the identity function, g(x) = x.)

AND

Express the function in the form f g h. (Use only elementary functions, but not the identity function, g(x) = x.)

H(x) = 3 - 4^x^2

I am not sure how to start these or even what they are asking for...any help would be greatly appreciated!

2. ..

mod plz delete

3. Do these work?
$f(x) = \frac{{5 + x}}{{10 + x}}\,\& \,g(x) = \cos (x) - 5$

4. Hello,l ryan18!

I think I understand the problem . . .

Express the function in the form $f \circ g$

. . $u(t) \;=\;\frac{\cos(t)}{5+\cos(t)}$

. . $\begin{array}{ccc}f(t) &=& \dfrac{t}{5+t} \\ \\[-3mm] g(t) &=& \cos(t) \end{array}$

Express the function in the form $f\circ g \circ h$

. . $\begin{array}{ccc}f(t) &=&\dfrac{t-5}{t} \\ \\[-3mm] g(t) &=& 5 + t \\ \\[-3mm] h(t) &=& \cos(t) \end{array}$

5. Originally Posted by ryan18
Express the function in the form f g h. (Use only elementary functions, but not the identity function, g(x) = x.)

H(x) = 3 - 4^x^2
$h(x) = x^2$

$g(x) = 4^x$

$f(x) = 3 - x$

$f[g[h(x)]] = f[g(x^2)] = f(4^{x^2}) = 3-4^{x^2}$