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C3 Condensed Notes
Functions:
Function= one-to-one or many-to-one mapping
Domain = all the possible inputs
Range = all the possible outputs
Inverse of functions: notated f 1(x)
Found by rearranging to make "x'' the subject, then switching "x" and ''y"
A function only has an inverse if it is a one-to-one mapping; if it's many-to-one,
restrict it's domain to make it a one-to-one mapping
e
...
for y = Y!-, restrict domain to x 2!:: 0
Domain and range of a function are switched when you inverse it
1
Geometrically, f (x) is f(x) reflected in y = x, so to find where f(x) = f 1(x), solve f(x) =
x or f 1 (x) = x

Modulus:
something = something else
e
...
2x - 1 = 6
find critical value: I 2x - 1 I so x = ½
sub back in and find when mod function multiplies by - 1 (in this case, x < ½)
ifx>½
ifx< ½
2x - 1 = 6
- 2x + 1 = 6
I something I = Isomething else I , then square both sides

I

I
I

I

Modulus inequalities:
o First, solve the inequality: set each side equal
o Find the critical value inequalities (there might be overlap here)
o Set up equations for each critical value inequality
o Check the solution to each equation is valid with the critical value inequality
used
o Sub a number less and greater than each solution into the original inequality
to find the final solution
C3 Trig

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