Easy Functions Problem

g(3)=12 ; fog(3)=f(g(3))=35

$f \text{ } o \text{ }g(3)$ really means ' function f of function g of 3 ', or $f(g(3))$ . So this can be easily solved.

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$f(g(3)) = f(15-3)$

$f(15-3) = f(12)$

$f(12) = 3(12)-1$

$36-1 = 35$

So our answer is $\boxed{35}$ !

we know if .. f o g (3) = f(g(3))

f(x) = 3x-1

g(x) = 15-x

g(3) = 12 f(g(3))= f(12) = 3(12) -1 = 35

or.. f o g (x) = f(g(x))

f o g (x) = f(15-x) = 3(15-x)-1 = 45-3x-1 = 44-3x

then change x as 3

f o g (3) = 44 - 3(3) = 44-9 = 35

It took me 20 minutes to figure out that $f o g(3)=f(g(3))$ , but when I did, the problem became easy:

$f o g(3)=f(g(3))=f(15-3)=f(12)=3(12)-1=36-1=\boxed{35}$