Question 3: (3+3+4+5 marks) a. Given f(x) = x² + 4 and g(x) = ?x - 5. Find (f o g) (x) and write the domain of (f o g) (x) in interval form. b. Divide: \frac{2xy}{x²y+3xy} + \frac{4x+12}{x²+6x+9} c. Solve: 0 = ?2x + 6 - ?3x - 4 d. Solve the inequality. (3x + 5)(x + 2) > 0 Question 4: (6 + 4 + 5 marks) a. Consider the parabola f(x) = -x² - 4x - 7 i) Write the equation in vertex form. ii) Find the vertex and axis of symmetry. e. Find the x-intercept and the y-intercept.
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To find (f o g)(x), we need to substitute g(x) into f(x). So, (f o g)(x) = f(g(x)) = f(x-5) = 2(x-5) + 4 = 2x - 10 + 4 = 2x - 6. To find the domain of (f o g)(x), we need to consider the domain of g(x) and the resulting function (f o g)(x). The domain of g(x) is Show more…
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