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I can help you solve or explain any of the questions from the image you provided. Below is a summary of the key problems from the paper:

1. Solve the following equations using suitable methods:
   a. \( \frac{2}{x} - \frac{x - 2}{x^2} = \frac{1}{3x} - \frac{2}{3} \)
   b. \( \frac{1}{1 + \frac{1}{x}} = \frac{1}{1 - \frac{1}{x}} \)
   c. \( \log{2} + \log(x + 2) - \log(3x - 5) = \log{3} \)
   d. \( 2x^2 - x - 2 < 0 \)

2. Find the domain and range of the following functions:
   a. \( f(x) = 1 + 8x - 2x^2 \)
   b. \( f(x) = \frac{1}{x^2 - 5x + 6} \)
   c. \( f(x) = \sqrt{x^2 - 6x + 8} \)

3. Show whether the following functions are one-to-one, onto, or neither:
   a. \( f: \mathbb{R} \to \mathbb{R}, \, f(x) = |x| \)
   b. \( f: \mathbb{R} \to \mathbb{R}, \, f(x) = x^2 \)

4. Find \( b \) and \( c \) given that the graph of \( y = x^2 + bx + c \) passes through the points (3, 14) and (-4, 7).

5. Show that \( 3 + \sqrt{5} \) is irrational and simplify \( x (\log_y{\log z}) \).

6. Let \( f(x) = 14x - 23 \), \( g(x) = \frac{1}{x^2} \), \( h(x) = x^2 - x \). Find \( f(g(x)), g(2), h(h(10)) \).

7. Draw the graph of the following functions:
   a. \( f(x) = x^4 - x^3 - 4x^2 + x + 1 \)
   b. \( f(x) = \frac{x}{3x^2} \)
   c. \( f(x) = \frac{x - 2}{(x - 1)(x + 1)} \)

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Solve the following mathematical problems from the provided image.

This webpage provides step-by-step solutions for problems involving algebraic equations, logarithmic identities, and quadratic inequalities. Additionally, it covers how to determine the domain and range of functions and graph them, suitable for Grades 10-12.

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