Function Composition Quiz

Function Composition

• Function f(x) is defined as f(x) = (x-3)/(√(x²-1)), where x² ≠ 1
• Function g(x) is defined as g(x) = 1/(∛x) , where x ≠ 0
• The domain of f(x) is all real numbers except x = ±1
• The domain of g(x) is all real numbers except x = 0
• The composite function fog(x) is calculated as f(g(x))
• fog(x) = (g(x) - 3) / √(g(x)² - 1)
• Substituting g(x) into the expression for fog(x) gives (1/∛x - 3)/√((1/∛x)² - 1)
• This simplifies to (1 - 3∛x)/√(1/∛x² - 1)
• The composition gof(x) is calculated as g(f(x))
• gof(x) = 1/∛f(x)
• Substituting f(x) into the expression for gof(x) gives 1/∛((x-3)/(√(x²-1)))
• Simplifying gives ∛(√(x²-1))/(x-3)

Test your understanding of function composition with this quiz on f(x) and g(x). You'll explore the calculation of fog(x) and gof(x), and see how to simplify these composite functions. Perfect for those studying advanced algebra concepts.