1. +919699990699,ersingh@hotmail.com Higher Level Mathematics
1. Find the largest domain for the function f : x  1 .
4  9x 2
2. Solve, for x, the equation log2 (5x2 – x – 2) = 2 + 2 log2 x.
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3. Let f : x  – 2 . Find
x2
(a) the set of real values of x for which f is real and finite;
(b) the range of f.
2x 1
4. The function f : x  , x , x  1. Find the inverse function, f –1, clearly stating
x –1
its domain.
5. Find the values of x for which 5 – 3x   x + 1.
2x – 1
6. The one-one function f is defined on the domain x > 0 by f (x) = .
x2
(a) State the range, A, of f.
(b) Obtain an expression for f –1(x), for x  A.
7. Solve the inequality x – 2  2x + 1.
x2 – 1
8. The function f is defined for x  0 by f (x) = .
x2 1
Find an expression for f –1(x).
x4 x–2
9. Let f (x) = , x  –1 and g (x) = , x  4.
x 1 x–4
Find the set of values of x such that f (x)  g (x).
10. Solve the inequality
x9
2
x9
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2. +919699990699,ersingh@hotmail.com Higher Level Mathematics
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11. (a) Find the largest set S of values of x such that the function f (x) = takes
3  x2
real values.
(b) Find the range of the function f defined on the domain S.
12. Find the range of values of m such that for all x
m(x + 1)  x2.
x4 x2
13. Let f (x) = , x ≠ –1 and g (x) = , x ≠ 4. Find the set of values of x such that
x 1 x4
f (x)  g (x).
8x  4
14. Find the largest set of values of x such that the function f given by f (x) =
x 3
takes real values.
15. Solve ln ( x  3) = 1. Give your answers in exact form.
p
16. Solve the equation 9 log5 x = 25 logx 5, expressing your answers in the form 5 , where q
p, q .
3x  4
17. The function f is defined as f (x) = , x  –2.
x2
(a) Find an expression for f −1(x).
(b) Write down the domain of f −1.
18. The solution of 22x+3 = 2x+1 + 3 can be expressed in the form a + log2 b where a, b .
Find the value of a and of b.
19. Solve 2 (ln x)2 = 3ln x −1 for x. Give your answers in exact form.
20. The functions f and g are defined as:
f (x) = e x , x  0
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g (x) = , x   3.
x 3
(a) Find h (x) where h (x) = g ◦ f (x).
(b) State the domain of h−1 (x).
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3. +919699990699,ersingh@hotmail.com Higher Level Mathematics
(c) Find h−1 (x).
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