1

If $f(x) = x^2$ and $g(x) = \sqrt{x+4}$

What is $g \circ f (3)$ ?

$g(f(x))$ would be $(\sqrt{x^2+4})(3)$ correct?

What would be my next move in figuring this out?

egreg
  • 238,574
SenzuBean
  • 61
  • 1
    First evaluate $f(3)=z$ then plug the result into $g$, then you get the result $(g \circ f)(3)=g(z)$... – Listing Dec 07 '13 at 16:49
  • @SenzuBean : $(\sqrt{x^2+4})(3)$ is really, really bad notation, at least for math (maybe in some computer languages people would write that). No math person would write that. A popular alternative that conveys what you mean is $\sqrt{x^2+4} \Big|_{x=3}$ – Stefan Smith Dec 08 '13 at 08:46

1 Answers1

3

suppose $f(x)=x^2=X$, $(g\circ f)(x)= g(f(x))=g(X)=\sqrt{X+4}=\sqrt{x^2+4}\Rightarrow (g\circ f)(3)=\sqrt{3^2+4}$

Myshkin
  • 35,974
  • 27
  • 154
  • 332