functions of graphs + modulus etc

Question 1

state whether there are solutions

Answer 1

there are no solutions as the graphs do not intersect

Question 2

Answer 2

The value for x cannot be negative as it equals a modulus which is ≥ 0

Answer 3

Question 4

graph of e^-x

Answer 4

Question 5

Answer 5

black= equal sign under inequality

white= no equal sign

Question 6

note

f(a) means that

Answer 6

YOU REPLACE “a” WITH “X” GODAMMMIT

Question 7

how do you know if something is a one to one function or not ?

Answer 7

draw horizontal line through function, if its not a 1 to 1 function, horizontal line cross 2 TIMES

Question 8

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

Answer 8

ln (x+3)^3

ALSO STATE THE FG(X) >

do not state that Y >

Question 9

F^2 (X)

Answer 9

ff(X)

Question 10

what is a root ?

Answer 10

where x = 0

Question 11

(modulus of x) < 1/4 = …..

Answer 11

-/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

Question 12

domain= range if function inverses ( they switch)

Question 13

if range = f(x)> -5

then domain is….

Answer 13

x>-5

Question 14

note : most inverse functions are just reflected in the line y=x

Answer 14

Question 15

set notation

Answer 15

Question 16

-f(x) and f(-x) respectively

Answer 16

y axis reflect, x axis reflect

Answer 17

Question 18

give a reason why h^-1(x) does not exist

Answer 18

h(x) is many-to-one, therefore h–1 (x) would be one-to-many, and so would not be a function.

Question 19

8c)

Answer 19