$\begin{aligned} f (2 x) + g (x - 1) & = 5 - 2 x + 3 x + 4 \\ = x + 9 \end{aligned}$
Answer $x + 4$
28 (b) Solve $g^{- 1} (x) = 2 x$
$\begin{array}{l} f (x) = x + 2 \\ f^{- 1} (x) = 4 \end{array}$
$f (4) = x$
$= 4 + 2$
[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

Answer

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Answer

$g^{- 1} (x) = 5$

Steps

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

Step 2 ： $g (x - 1) = (x - 1) + 1 = x$

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

Step 4 ： $5 x - 3 = x + 9$

Step 5 ： $4 x = 12$

Step 6 ： $x = 3$

Step 7 ： $g^{- 1} (x) = y$

Step 8 ： $g (y) = 2 x$

Step 9 ： $y + 1 = 2 x$

Step 10 ： $y = 2 x - 1$

Step 11 ： $g^{- 1} (x) = 2 (3) - 1 = 5$

Step 12 ： $g^{- 1} (x) = 5$