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Mathematics Past Questions and Answers

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Mathematics Questions

Question 356:

Given that \(f : x \to \frac{2x - 1}{x + 2}, x \neq -2\), find \(f^{-1}\), the inverse of f.

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A \(f^{-1} : x \to \frac{1+2x}{2-x}, x \neq 2\)
B \(f^{-1} : x \to \frac{1-2x}{x+2}, x \neq -2\)
C \(f^{-1} : x \to \frac{1-2x}{x-2}, x \neq 2\)
D \(f^{-1} : x \to \frac{1+2x}{x+2}, x \neq -2\)

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Question 357:

Simplify \(\frac{1 - 2\sqrt{5}}{2 + 3\sqrt{2}}\).

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A \(14(2\sqrt{2} + 6\sqrt{5} - 4\sqrt{10})\)
B \(\frac{1}{14}(2 - 3\sqrt{2} - 4\sqrt{5} - 6\sqrt{10})\)
C \(\frac{1}{14}(3\sqrt{2} + 4\sqrt{5} - 6\sqrt{10} - 2)\)
D \(14(2 + 3\sqrt{2} - 6\sqrt{5} + 4\sqrt{10})\)

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Question 358:

Solve: \(2\cos x - 1 = 0\).

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A \((\frac{2\pi}{3}, \frac{4\pi}{3})\)
B \((\frac{\pi}{6}, \frac{5\pi}{6})\)
C \((\frac{\pi}{5}, \frac{2\pi}{5})\)
D \((\frac{\pi}{3}, \frac{5\pi}{3})\)

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Question 359:

Solve: \(4(2^{x^2}) = 8^{x}\)

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A (1, 2)
B (1, -2)
C (-1, 2)
D (-1, -2)

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Question 360:

If \(\log_{3} x = \log_{9} 3\), find the value of x.

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A \(3^{2}\)
B \(3^{\frac{1}{2}}\)
C \(3^{\frac{1}{3}}\)
D \(2^{13}\)

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