F.4 Maths

1. Consider f(x) = x^2 + 3x + k, where k is a constant. If f(k) = 21,
find the values of k.

f(x) = k^2 + 3k + k = 21
k^2 + 3k + k – 21 = 0
k^2 + 4k – 21 = 0
(k + 7)(k - 3) = 0
k = -7 or k = 3

2. If f(x) = 2x + 3 and m = f(1), find the values of
a. m b. f(m)

a. m = 2(1) + 3
m = 5
b. f(m) = 2(5) + 3
f(m) = 13

3. If f(x) = 5 - 6x and k = f {2/3}, find the values of
a. k b. f(k)

a. k = 5 – 6(2/3) = 5 – 4
k = 1
b. f(k) = 5 - 6(1)
f(k) = -1

4. If f(x) = 4 - 3x and f(a) = -11, find the value of a

f(a) = 4 – 3a = -11
3a = 4 + 11= 15
a = 15/3
a = 3

5. If h(x) = 5 + 2x and h(u^2) = 13, find the values of u.

h(x) = 5 + 2x
h(u^2) = 5 + 2(u^2) = 13
2u^2 = 13 – 5 = 8
u^2 = 8/2 = 4
u = 2 or - 2

6. Consider f(x) = 9/2x-5 , where x ≠ 5/2, If f(a) = 3, find the value of a.

It is assumed the function is 9 is divided by 2x, then minus 5, not (9/2)x - 5
f(x) = 9/2x-5
f(a) = 9/2a -5 = 3
9/2a = 3 + 5 = 8
a = 9/16

7. If f(x) = x^2 - 3x = 4 and f(k+1) = 4, find the values of k

f(x) = x^2 - 3x = 4 This statement is not true
It means whatever value of x, f(x) = 4, say we put x = 1, f(1) = (1)^2 – 3(1) = -2

If f(x) = x^2 - 3x + 4 (Assume typo error, “=” replaced by “+”)
f(k+1) = (k+1)^2 – 3(k+1) + 4 = 4
k^2 + 2k + 1 -3k – 3 = 0
k^2 –k -2 = 0
(k -2)(k +1) = 0
k = 2 or k = -1