composing functions

**lemontea** · May 12th 2008, 12:09 PM

1) Find the functions f and g so that gof.
h(x)= 1/(sqrt(x^2)-4)

**Moo** · May 12th 2008, 12:19 PM

Hello,

Originally Posted by lemontea

1) Find the functions f and g so that gof.
h(x)= 1/(sqrt(x^2)-4)

What about f(x)=sqrt(x^2)-4
And g(t)=1/t

?

**earboth** · May 12th 2008, 12:25 PM

Originally Posted by lemontea

1) Find the functions f and g so that gof.
h(x)= 1/(sqrt(x^2)-4)

...

I'll show you a few possibilities: $h(x)=g(f(x))$

$\begin{array}{lcr}g(x)=\frac1x & \text{and} & f(x)=\sqrt{x^2}-4 \\<br /> g(x)=\frac1{\sqrt{x}-4} & \text{and} & f(x)=x^2 \\<br /> g(x)=\frac1{x-4} & \text{and} & f(x)=\sqrt{x^2} \end{array}$

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