Core Pure -as Year 1- Unit Test 5 Algebra And Functions -

As she walked out, she thought: That wasn't a test. That was a rite of passage.

Elena set her pen on the desk. Her palms were damp, but her mind was clear. She had faced the domain restrictions, the partial fraction decomposition, the inverse function trap, the composite’s hidden conditions, and the elegant emptiness of the squared inequality. core pure -as year 1- unit test 5 algebra and functions

On her desk lay . The front cover was deceptively calm, featuring only the exam board’s logo and the instruction: Attempt all questions. Use algebraic methods unless otherwise stated. As she walked out, she thought: That wasn't a test

was the function composition trap. Given ( h(x) = \sqrt{x+4} ) for ( x \geq -4 ), and ( k(x) = x^2 - 1 ) for ( x \geq 0 ). Find ( h(k(x)) ) and state its domain. She composed carefully: ( h(k(x)) = \sqrt{(x^2 - 1) + 4} = \sqrt{x^2 + 3} ). Wait, she thought. That’s defined for all real ( x ), but ( k ) only takes ( x \geq 0 ). And ( k(x) ) gives outputs ( \geq -1 ), but ( h ) requires inputs ( \geq -4 ). That’s fine. Her palms were damp, but her mind was clear