\[ \begin{aligned} f(2 x)+g(x-1) & =5-2 x+3 x+4 \\ & =x+9 \end{aligned} \] Answer $x+4$ 28 (b) Solve $\mathrm{g}^{-1}(x)=2 x$ \[ \begin{array}{l} f(x)=x+2 \\ f^{-1}(x)=4 \end{array} \] \[ f(4)=x \] \[ =4+2 \] [3 marks] Let $g^{-1}(x)=y$ \[ \begin{aligned} y & =2 x \\ x & =\frac{y}{2} \\ g(x) & =\frac{x}{2} \\ & = \\ , x & =4 x \end{aligned} \] \[ x=4 x \] \[ 4 x \] END OF QUESTIONS 29

Step 1 ：\(f(2x) = 2(2x) - 3 = 4x - 3\)

Step 2 ：\(g(x-1) = (x-1) + 1 = x\)

Step 3 ：\(f(2x) + g(x-1) = (4x - 3) + x = 5x - 3\)

Step 4 ：\(5x - 3 = x + 9\)

Step 5 ：\(4x = 12\)

Step 6 ：\(x = 3\)

Step 7 ：\(g^{-1}(x) = y\)

Step 8 ：\(g(y) = 2x\)

Step 9 ：\(y + 1 = 2x\)

Step 10 ：\(y = 2x - 1\)

Step 11 ：\(g^{-1}(x) = 2(3) - 1 = 5\)

Step 12 ：\(g^{-1}(x) = \boxed{5}\)