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Functions The domain is what x can be The range is what y can be Inverse Functions f −1 ( x) To find an inverse function: 1. Switch x and y 2. Rearrange to make y the subject On a graph it is a reflection in the line y = x Composite Functions f (x ) g ( x) fg ( x) means put g into f gf (x) means put f into g The Exponential and Logs y=e x 1 y=ln ( x) 1 ln( x) means log e x ln( x)is the inverse of e x Iteration U n+1 =√U n + 5 U 0=2 U 1=√(2)+5=√ 7 U 2=√( √7)+5=2.765(3dp) U 3=√ ( ANS )+5=2.787( 3dp) U 4=√( ANS )+ 5=2.790(3dp) U 5=√( ANS )+5=2.791( 3dp) U 6=√( ANS )+5=2.791( 3dp) f ( x )=0 has a solution between a and b if f ( a)and f ( b) have different signs Transforming Graphs y= f ( x ) (4,3) x 1 x (-2,-2) y= ∣ f ( x) ∣ (4,3) x (-2,2) x 1 y= f (∣ x ∣) (4,3) x (-4,3) x 1 Trigonometry 1 =cosec(θ) sin(θ) 1 =sec (θ) cos(θ) 1 =cot(θ) tan(θ) 2 2 cos θ +sin θ=1 2 2 1+tan θ=sec θ 2 2 1+cot θ=cosec θ sin(θ) = sin(180−θ) cos (θ) = sin(360−θ) tan (θ) = tan(θ+180) Trigonometry In the Formula Book sin( A± B)=sinAcosB±cosAsinB cos ( A±B)=cosAcosB∓sinAsinB tanA±tanB tan (A±B)= 1∓tanAtanB Not in the Formula Book (but you can make them by substituting B for A) sin(2A)=2sinAcosB cos (2A)=cos 2 A−sin2 A 2tanA tan (2A)= 2 1−tan A To put something in the form R sin(θ±α) or R cos(θ∓α): -Compare to compound angle formula 2 2 2 -Find R using pythagoras: R =a + b -Find alpha by dividing sin by cos to get tan Differentiation Chain Rule dy du dy = × dx dx du Product Rule y=uv dy du dv =v + u dx dx dx Quotient Rule u y= v du dv v −u dy dx dx = 2 dx v Differentiation Function e x Derivative e x ln( x) 1 x sin( x) cos ( x) cos ( x) −sin (x )