\[
\begin{aligned}
f(2 x)+g(x-1) & =5-2 x+3 x+4 \\
& =x+9
\end{aligned}
\]
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 ：\(g^{-1}(x) = \boxed{5}\)