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Function - Summer Term

The document contains a series of mathematical problems related to functions, including finding values of functions at specific points, solving equations, and expressing functions in terms of others. It is divided into two levels, with Level 1 focusing on basic function evaluations and Level 2 introducing more complex relationships and equations. Each problem requires applying algebraic techniques to derive solutions.

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wkyu20030123
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7 views2 pages

Function - Summer Term

The document contains a series of mathematical problems related to functions, including finding values of functions at specific points, solving equations, and expressing functions in terms of others. It is divided into two levels, with Level 1 focusing on basic function evaluations and Level 2 introducing more complex relationships and equations. Each problem requires applying algebraic techniques to derive solutions.

Uploaded by

wkyu20030123
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Functions (Summer Term)

Level 1
1. If f(x) = –4x2 + 3x, find the values of 7. If g(x) = 1 – (x + 1 )(x – 2), find the
the function when values of g(x) when
(a) x = –1 (a) x = 2
1 (b) x = 0
(b) x = 2
(c) x = –4

2. If f(x) = 2x2 + x, find the values of


𝑎 8. It is given that f(x) = (x + 3)(kx – 3)
(a) f( )
3
and g(x) = (x – 1)(x +6).
(b) f(b – 3)
(a) If f(3) = 18, find the value of k.
(b) If h(x) = g(2x), express h(x) in
3. If f(x) = kx – x2 and f(5) = –5, find the
terms of x.
values of
(c) Solve the equation 2f(x) – h(x) = 0.
(a) k
(b) f(–5) 1
9. If h(x) = 𝑎𝑥 + 2𝑥 2 and h(5) = 100, find

1 the value of a.
4. If h(x) = x + 𝑥 2 −1, find the values of

(a) h(–2) 𝑥−5


10. If h(x) = 𝑥+5, find the values of
(b) h(0)
(c) h(2) (a) h(0)
(b) h(a + 5)
1
5. If f(x) = 2x + 5, find the values of the (c) h(𝑏)
function when
(a) x = 0 11. It is given that f(x) = ax2 + 2x + 1 and
(b) x = 5 g(x) = x2 + 3x.
(c) x = –3 (a) If f(–2) = 1, find the value of a.
(b) If h(x) = g(x – 1), express h(x) in
6. It is given that f(x) = 3x2. terms of x.
(a) Find the values of f(1) and f(2). (c) Solve the equation f(x) = h(x) + 2.
(b) Does the relation f(1) + f(1) = f(2)
hold?
Level 2
12. It is given that g(x) = 4x – 9. Find the 20. It is given that f(x) = ax2 + bx +3.
1 (a) If f(–1) = 1 and f(3) = 33, find the
values of x if g(x) – g(𝑥) = 0.
values of a and b.
𝑥
13. It is given that f(x) = (x + 2k)2 and (b) If g(2) = f(x), express g(x) in terms

g(x) = 5k + x. of x.
(a) If f(0) – 3g(3) = k – 25 , find the (c) Hence, find the values of g(5) and
value of k. g(p – 1).
(b) Solve the equation f(x) – 2g(x) = 3.
21. It is given that g(x) = 2x2 + 5x – 3 and
1 1
14. If f(x) = x2 – 𝑥 2 , show that f(𝑥) = – f(x). g(x) = f(x – 2).
(a) Solve g(x) = 0.
(b) Hence, solve f(x) = 0.
15. If f(x) = x2 + 3x – 15, find the values of
(a) f(3)
22. It is given that f(x) = 4x2 – 12x + 9 and
(b) f(–a)
g(x) = f(x +3).
(c) f(2b + 1)
(a) Solve f(x) = 0.
(b) Hence, solve g(x) = 0.
16. It is given that f(x) = (x + k)(x – 1) – 2x
and f(k) = k2 – 3. Find the value(s) of k.

17. It is given that f(x) = (x – a)(x – b) + 5.


If f(a) = b and f(2b) = 3b, find the
values of a and b.

𝑥−1 2
18. Let g(x) = (𝑥+1) .
𝑥−1
(a) Find g(𝑥+1).
5
(b) Hence, find the value of g(7).

19. It is given that f(x) = 𝑥 2 − 3𝑥 + 2.


(a) Find the values of f(2a) and f(a +2)
(b) If f(2a) = f(a + 2) + 2f(a), find the
value(s) of a.

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