# which is the function of (3) based in this equation

If we know that $(f\circ f)(x)=4x+3$, with $f(0)=4$, what is $f(3)=?$

I have found that $f(f(x))= 16x+15$, but I don't know where to go from there.

• This is not clear. What's the difference between $f\circ f(x)$ and $f[f(x)]$? – lulu Mar 26 '18 at 19:12
• I don't understand the part about $16x+5$. For the earlier part, note that $f\circ f(0)=3\implies f(f(0))=3\implies f(4)=3\implies f\circ f(4)=f(3)$. Can you finish from there? – lulu Mar 26 '18 at 19:16
• how did you find that f(4)=3 – Lyds Mar 26 '18 at 19:23
• We know that $f(f(0))=3$ and $f(0)=4$. – lulu Mar 26 '18 at 19:23
• so how does that help us? – Lyds Mar 26 '18 at 19:32

Notice that $$f(0)=4$$ and $$f(f(0))=3$$, so $$f(4)=3$$ which implies $$f(3)=f(f(4))=19$$.