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It seems you've uploaded a math problem sheet with various questions. I'll guide you through them step by step. Let's begin by listing the problems, and then you can choose which one you'd like to solve first:

1. Solve the following equations using suitable methods:
   - (a) \( \frac{2}{x} - \frac{x}{x^2 - 2x} = 1 - \frac{2x - 2}{3x - 2} \)
   - (b) \( \frac{1}{1 + \frac{1}{x}} - \frac{1}{x + 1} = \frac{x + 1}{x - 2} \)
   - (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) \( f(x) = \frac{1 + 8x - 2x^2}{1} \)
   - (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 \( x^{\log_2 x - \log_2 2}, y^{\log_2 y - \log_2 2}, z^{\log_2 z - \log_2 9} = 1 \).

6. Let \( f(x) = 14x - 23, g(x) = \frac{1}{x^2}, h(x) = x^2 - x \). Find:
   - \( (f \circ g)(x + 1) \)
   - \( f(20), g(2), h(100), h(10) \)

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

Let me know which specific problem you'd like to work on, and I can help you solve it!

Solve equations, find domain and range, analyze functions, find coefficients, and sketch graphs for various algebraic and transcendental functions.

This problem set includes solving equations with logarithms and quadratics, determining domain and range, analyzing one-to-one and onto functions, and graphing complex algebraic functions. Ideal for Grades 10-12 students.

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