| Exam Board | Edexcel |
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| Module | PMT Mocks (PMT Mocks) |
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| Topic | Composite & Inverse Functions |
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5. The function f is defined by
$$\mathrm { f } : x \rightarrow \frac { 2 x - 3 } { x - 1 } \quad x \in R , x \neq 1$$
a. Find \(f ^ { - 1 } ( 3 )\).
b. Show that
$$\mathrm { ff } ( x ) = \frac { x + p } { x - 2 } \quad x \in R , \quad x \neq 2$$
where \(p\) is an integer to be found.
The function g is defined by
$$g : x \rightarrow x ^ { 2 } - 5 x \quad x \in R , 0 \leq x \leq 6$$
c. Find the range of g .
d. Explain why the function g does not have an inverse.