Core Pure -as Year 1- Unit Test 5 Algebra And Functions May 2026

brought the first real resistance. The function ( g(x) = \frac{3x+1}{x-2} ), ( x \neq 2 ). Find ( g^{-1}(x) ) and state its domain. She swapped ( x ) and ( y ): ( x = \frac{3y+1}{y-2} ). Cross-multiplied: ( x(y-2) = 3y+1 ). ( xy - 2x = 3y + 1 ). Grouped terms: ( xy - 3y = 2x + 1 ). Factored: ( y(x-3) = 2x+1 ). So ( g^{-1}(x) = \frac{2x+1}{x-3} ).

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

She wrote the final answer: ( \sqrt{x^2+3} ), domain ( [0, \infty) ). brought the first real resistance

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 ). She swapped ( x ) and ( y ): ( x = \frac{3y+1}{y-2} )

Elena stared at the clock on the wall of Exam Hall 4. 9:02 AM. She had 58 minutes left.

She turned the page.