F(3) = 9 f'(3) = 3 L(x) = linear approximation to f(x) at x = a L(x) = linear approximation to f(x) at x = 3 L(x) = f'(a)*(x-a)+f(a) L(x) = f'(3)*(x-3)+f(3) L(x) = 3*(x-3)+9 L(x) = 3x-9+9 L(x) = 3x L(3.02) = 3*3.02 L(3.02) = 9.06 So f(3.02) is approximately 9.06 based on the L(x) linear approximation
g(9) = 3 g'(9) = 5 M(x) = linear approximation to g(x) at x = 9 M(x) = linear approximation to g(x) at x = a M(x) = g'(a)*(x-a)+g(a) M(x) = g'(9)*(x-9)+g(9) M(x) = 5*(x-9)+3 M(x) = 5x-45+3 M(x) = 5x-42 M(9.06) = 5*9.06-42 M(9.06) = 3.3
So g(9.06) is approximately equal to 3.3 based on the linear approximation M(x)
In summary, this means g(9.06) = g(f(3.02)) = 3.3 which are approximations
