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# 1.7.3 Function, SPM Practice (Long Question)

Question 5:
In diagram below, the function g maps set P to set Q and the function h maps set Q to set R. Find
(a) in terms of x, the function
(i) which maps set Q to set P,
(ii) h(x).
(b) the value of x such that gh(x) = 8x + 1.

Solution:
(a)(i)

(a)(ii)

(b)

Question 6:
(a) the value of m, [2 marks]
(b)   gf-1(–2), [3 marks]
(c) function h if hg (x) = 12x + 5 [3 marks]

Solution:
(a)
$\begin{array}{l}mx-3=0\\ m\left(\frac{3}{2}\right)-3=0\\ m=3×\frac{2}{3}=2\end{array}$

(b)

$\begin{array}{l}g{f}^{-1}\left(-2\right)=g\left(\frac{2}{3}\right)\\ \text{}=3-4\left(\frac{2}{3}\right)\\ \text{}=\frac{1}{3}\end{array}$

(c)
hg (x) = 12x + 5
h [g(x)] = 12x + 5
(3 – 4x) = 12x + 5
Let u = 3 – 4x
$\begin{array}{l}x=\frac{3-u}{4}\\ h\left(u\right)=12\left(\frac{3-u}{4}\right)+5\\ h\left(u\right)=9-3u+5\\ h\left(u\right)=14-3u\\ h\left(x\right)=14-3x\end{array}$

### 2 thoughts on “1.7.3 Function, SPM Practice (Long Question)”

1. (a)(1)
g-1(x)= x-2 over 3

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