Algebra, MET2 2007 VCAA 2 MC Let `g(x) = x^2 + 2x - 3 and f(x) = e^(2x + 3).` Then `f(g(x))` is given by `e^(4x + 6) + 2 e^(2x + 3) - 3` `2x^2 + 4x - 6` `e^(2x^2 + 4x + 9)` `e^(2x^2 + 4x - 3)` `e^(2x^2 + 4x - 6)` Show Answers Only `D` Show Worked Solution `text(Solution 1)` `text(Define)\ \ f(x) and g(x)\ \ text(on CAS)` `f(g(x)) = e^(2x^2 + 4x – 3)` `=> D` `text(Solution 2)` `f(g(x))` `=e^(2 xx (x^2 + 2x – 3)+3)` `= e^(2x^2 + 4x – 3)` `=>D`
Algebra, MET2 2010 VCAA 4 MC If `f(x) = 1/2e^(3x) and g(x) = log_e(2x) + 3` then `g (f(x))` is equal to `2x^3 + 3` `e^(3x) + 3` `e^(8x + 9)` `3(x + 1)` `log_e (3x) + 3` Show Answers Only `D` Show Worked Solution `text(Define)\ \ f(x)= 1/2e^(3x), \ g(x)= log_e(2x) + 3` `g(f(x))` `= log_e(2 xx 1/2e^(3x)) + 3` `=log_e e^(3x) + 3` `=3x + 3` `= 3 (x + 1)` `=> D`