If the function f is defined by f(x + 2) = 2x\(^2\) + 7x - 5, find f(-1)
-10
-8
4
10
Correct answer is B
f(x + 2) = f(-1)
f(-1) is gotten when x = -3.
\(2x^{2} + 7x - 5\) at x = -3.
f(-1) = \(2(-3)^{2} + 7(-3) - 5\)
= \(18 - 21 - 5 = -8\)
Solve the following equation (3x - 2)(5x - 4) = (3x - 2)2
\(\frac{-2}{3}\), 1
1
\(\frac{2}{3}\), 1
\(\frac{2}{3}\), \(\frac{4}{5}\)
Correct answer is C
(3x - 2)(5x - 4) = (3x - 2)2 = 5x2 - 22x + 6
= 9x2 = 12x + 4
6x2 - 10x + 4 = 0
6x2 - 6x - 4x + 4 = 0
6x(x - 1) -4(x - 1) = (6x - 4)(x -1) = 0
x = 1 or \(\frac{2}{3}\)
Solve the following simultaneous equation for x. x2 + y - 5 = 0, y - 7x + 3 = 0
-2, 4
2, 4
-1,8
1, -8
Correct answer is D
x2 + y - 5 = 0.....(i)
y - 7x + 3 = 0.........(ii)
y = 7x - 3, substituting the value of y in equation (i)
x2 + (7x - 3) - 5 = 0
x2 + 7x + 3 = 0
(x + 8)(x - 1) = 0
x = -8 or 1
Evaluate (x + \(\frac{1}{x}\) + 1)2 - (x + \(\frac{1}{x}\) + 1)2
4x2
(\(\frac{2}{x}\) + 2)2
4
4(1 + x)
Correct answer is D
(x + \(\frac{1}{x}\) + 1)2 - (x + \(\frac{1}{x}\) + 1)2
= (x + \(\frac{1}{x}\) + 1 + x + \(\frac{-1}{x}\) - 1)(x - \(\frac{1}{x}\) + 1 - x + \(\frac{1}{x}\) + 1)
= (2x) (2 + \(\frac{2}{x}\)) = 2x x 2(1 + \(\frac{1}{x}\))
4x (1 + \(\frac{1}{x}\)) = 4x + 4
= 4(1 + x)
Which of the following is a factor of 15 + 7x - 2x2
x + 3
x - 3
x - 5
x + 5
Correct answer is C
Factorize 15 + 7x - 2x2
(5 - x)(3 + 2x); suppose 15 + 7x = 2x2 = 0
∴ (5 - x)(3 + 2x) = 0
x = 5 or x = -\(\frac{3}{2}\)
Since 5 is a root, then (x - 5) is a factor