Maths

Question 1

Inverse functions

Answer 1

Example:
F(x) = 3x+2 find f-¹(x)

Let Y = f(x). Y=3x+2
-2 -2
Y-2=3x
/3 /3
(Y-2)/3 = x

     F-¹ (x) = (x-2)/3

Steps
Step One
- Make f(x) become Equal to Y
Step two
- Make X the subject
Step Three
- write the f-¹(x) in terms of x

Question 2

Surds

Answer 2

√a x√b = √ab

√a x √a = a

√a / √b = √a/b

Question 3

Completing the square

Answer 3

X²-2x-2=0

X²-2x=2

(X-1)²-1²=2

(X-1)²-1=2
(X-1)²=3

X=1±√3

Steps

Step one
-Move constant to the right

Step two
-half the nx number (e.g 2x goes to 1) and place inside in the n position (x±n)

Step three
Square the new n value and subtract it from the overall equation e.g (x-1)²-1²=2

Step four
Remove the -n number by adding or subtracting to get to 0 doing the same to the other side.

Step five
Square root both sides removing the (x)²

Step six
Add or subtract the final value in the x bracket, e.g 1±√3=x