Starter Easy (hopefully) sub values into functions card activity Harder one: A function is defined by : f(x) = (x+3)(x-5) Find the inverse and state the domain and range of f(x) and f -1 (x) A function is defined by : f(x) = (x-16)(x-4) Find the inverse and state the domain and range of f(x) and f -1 (x) Homework: Edpuzzle: Video on combined transformations and complete quiz New class code: ejRZ9Y Functions recap and consolidation Recap all work on functions. Go over harder inverse functions, particularly with e x and ln x Reinforce other harder inverse functions such as quadratics and algebraic fractions Inverse functions Inverse functions only exist for one-one functions. Things to note.. The domain of f -1 is the range of f and the range of f -1 is the domain of f. The graph of an inverse function can be found by reflecting a function in the line y=x Have a go: Functions and Inverses card match ppt: 10 questions MWB: Inverse functions with e x f(x) = e 2x x = e 2y x - 6 = e 2y-1 ln(x - 6) = ln e 2y-1 ln(x - 6) = 2y - 1 The inverse of f(x) is f -1 (x) = (ln(x-6) + 1) Domain ? ln(x - 6) +1 = 2y (ln(x - 6) +1) = y Domain is x > 6 Cannot have ln of numbers less than 0 MWB: Inverse functions with ln x f(x) = ln(2x) + 6 x = ln(2y) + 6 x - 6 = ln (2y) e x-6 = e ln 2y e x-6 = 2y The inverse of f(x) is f -1 (x) = e x-6 Domain ? e x-6 = y Have a Go General Functions questions 5 exam questions relay Skip modulus questions ppt: 10 questions Plenary Plenary f(x) = x. x+1 Show that f -1 (x) = x Extension: