I'm trying to find what the *g*$(f(2))$ and the f $(g(2))$ is.

Here are the functions for f and g:

Let A - $\{$1, 2, 3, 4$\}$ and B - $\{$a, b, c, d$\}$

  • Let f : A $\rightarrow$ B be defined so that f - $\{$$\lt$1, b$\gt$,$\lt$2, c$\gt$, $\lt$3, d$\gt$, $\lt$4, a$\gt$$\}$
  • Let g : B $\rightarrow$ A be defined so that g - $\{$$\lt$a, 1$\gt$,$\lt$b, 2$\gt$, $\lt$c, 4$\gt$, $\lt$d, 4$\gt$$\}$

This is what I've done so far, but i'm not sure if it's done correctly, please feel free to correct me.

$g(f(2))$ - We have $f(2)$ in g which is $f(2) = c$ and $g(c)$ which is $g(c) = 4$.

Is this done correctly or I'm I missing something out on this?

I'm not sure how i can solve the f $(g(2))$ would appreciate some help.

Thanks a lot

  • 2
    $\begingroup$ You did g(f(2)) correctly. You can't do f(g(2)) because g(2) isn't defined (2 isn't in the domain of g) $\endgroup$ – Tyler Oct 4 '13 at 18:49
  • $\begingroup$ ah great! thought I was doing it wrong. Alright yeah, that's what i was struggling with. Thanks for your answer! $\endgroup$ – Dabbish Oct 4 '13 at 18:50
  • $\begingroup$ I'll just add that as an answer then :) $\endgroup$ – Tyler Oct 4 '13 at 18:51

You did $g(f(2))$ correctly. You can't do $f(g(2))$ because $g(2)$ isn't defined since $2$ isn't in the domain of $g$.


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