Question

Show that the function defined by f:QQ:f(x)=3x + 5 for all x Є Q is one-one and onto. Find a formula for f -1.

Answer 1

last question first. this function says
1) multiply by 3
2) add 5

inverse says
1) subtract 5
2) divide by 3
\[f^{-1}(x)=\frac{x-5}{3}\]

Answer 2

k

Answer 3

to show it is one to one you have a choice. you can say
" it is a line and all lines are one to one (except horizontal ones) because they all pass the horizontal line test"

Answer 4

or you can say
Let
\[f(a)=f(b)\] and show what
\[a=b\] as follows
\[f(a)=f(b)=\]
\[3a+5=ab+5\iff 3a=ab\iff a=b\]

Answer 5

wow

Answer 6

u r a legend indeed

Answer 7

you also have a simple way to find the inverse if you do did not like my words. write
\[y=3x+5\] then switch x and y to write
\[x=3y+5\] solve for y get
\[x-5=3y\]
\[\frac{x-5}{3}=y\] so
\[f^{-1}(x)=\frac{x-5}{3}\] as before

Answer 8

how do we say its onto???/

Answer 9

u there???

Answer 10

onto?

Answer 11

ya

Answer 12

show that for any number "b" there is an "a" with
\[f(a)=b\] but you have already done this because you know if
that
\[a=\frac{b-5}{3}\]

Answer 13

wow thx a lott