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

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.

She felt a small smile. But the test wasn't done. core pure -as year 1- unit test 5 algebra and functions

Unit Test 5 wasn't just about algebra. It was about precision. About checking every assumption. About remembering that a square can never be negative. was the function composition trap

Elena stared at the clock on the wall of Exam Hall 4. 9:02 AM. She had 58 minutes left. She composed carefully: ( h(k(x)) = \sqrt{(x^2 -

was the killer. The one that separated the A from the B. The function ( p(x) = x^4 - 8x^2 + 16 ). Find all real roots. Hence solve the inequality ( p(x) < 0 ). She factorised: let ( u = x^2 ). Then ( u^2 - 8u + 16 = (u-4)^2 ). So ( p(x) = (x^2 - 4)^2 = (x-2)^2 (x+2)^2 ).