functions of graphs + modulus etc Flashcards
state whether there are solutions
there are no solutions as the graphs do not intersect
The value for x cannot be negative as it equals a modulus which is ≥ 0
graph of e^-x
black= equal sign under inequality
white= no equal sign
note
f(a) means that
YOU REPLACE “a” WITH “X” GODAMMMIT
how do you know if something is a one to one function or not ?
draw horizontal line through function, if its not a 1 to 1 function, horizontal line cross 2 TIMES
how else can 3ln (x+ 3) be written
IMPORTANT NOTE: LOOK AT THE QUESTION BELOW
i thought the ln cancelled out to 3ln(x+3)-1
but it actually wsa ln(x+3)^3 -1
ln (x+3)^3
ALSO STATE THE FG(X) >
do not state that Y >
F^2 (X)
ff(X)
what is a root ?
where x = 0
(modulus of x) < 1/4 = …..
-/14
the reason -1/4 is there is because if ypou sub it back into the original equation, it gives 1/4 which is not smaller than 1/4 ( as needed in original equation) so x has to be larger than “-1/4” so that modulus of x is smaller than 1/4
x also has to be smaller than 1/4 as the equation requires it to be smaller than 1/4
domain= range if function inverses ( they switch)
if range = f(x)> -5
then domain is….
x>-5
note : most inverse functions are just reflected in the line y=x
set notation
-f(x) and f(-x) respectively
y axis reflect, x axis reflect
give a reason why h^-1(x) does not exist
h(x) is many-to-one, therefore h–1 (x) would be one-to-many, and so would not be a function.
8c)
