3. y = f(x) = 3^(x-2) + 1;
y-1 = 3^(x-2),
y-1>0,
log_3 (y-1) = x-2;
x = 2+log_3 (y-1),
x = g(y) = 2 + log_3 (y-1),
g(x) = 2 + log_3 (x-1).
4. По условию log_2 (5) = a,
log_100 (40) = (log_2 (40) )/( log_2 (100) ) = (log_2 (5*8) )/( log_2 (25*4) ) =
= ( log_2 (5) + log_2 (8) )/( log_2 (25) + log_2 (4) ) =
= ( a + 3 )/( log_2 (5^2) + 2 ) = (a+3)/( 2*log_2 (5) + 2 ) = (a+3)/(2a+2).