Question

Write the inverse function for the function, ƒ(x) =1/2 x + 4. Then, find the value of ƒ^-1(4)

Answer 1

to find the inverse of a function

f(x)=x+3

we let f(x)=y
then we want to make x the subject

y=x+3
y-3=x

now we replace x with f^-1(x)
and replace y with x

f^-1(x)=x-3

Answer 2

so do the same for your question and let me know what you get

Answer 3

\[f(x)=\frac{ 1 }{ 2 }x + 4\]
ley y=f(x)

\[y=\frac{ 1 }{ 2 }x + 4\]

make x the subject

Answer 4

so x= 1/2 y +4

Answer 5

no

Answer 6

do you know how to rearrange equations?

Answer 7

not really and the notes i have don't really give me anything to work with

Answer 8

you need to understand that
addition
and subtraction
are opposite

multiply and divide are opposites

Answer 9

so if you have

Answer 10

y=x+3

Answer 11

make x the subject

Answer 12

you must subtract 3 on both sides

Answer 13

y-3=x

Answer 14

if you have y=2x+4

Answer 15

we subtract 4 on both sides,

y-4=2x

now we have 2 lots of x we want x on its own, so we must divide by 2

Answer 16

\[\frac{ 1 }{ 2 }(y-4)=x\]

Answer 17

so in your question

Answer 18

\[y=\frac{ 1 }{ 2 }x+4\]

Answer 19

can you make x the subject

Answer 20

so it would start with subtracting 4

y-4= 1/2 x

then divide 1/2

(y-4)/2=x

Am I close?

Answer 21

if you divide by 2 you are correct

you said divide by 1/2, which is equivalent to multiplying by 2

so you actually have

2(y-4)=x

Answer 22

so now that we have

2(y-4)=x

Answer 23

we replace x with f^-1(x)
and replace y with x

Answer 24

2(x-4)=f^-1(x)

this is our inverse function

Answer 25

so in the question it wanted you to find f^-1(4) in this function
so substitute x=4

Answer 26

ok so the function would look like

f^-1(4)=2(4-4)

then you would multiply the 2 into the parentheses, right?

Answer 27

well what is 4-4

Answer 28

0
so
f^-1(4)=0

Answer 29

yes well done! thank you for testimony but please can you give me a medal for best answer?

Answer 30

if you need more practice with inverse functions I can help you out, just let me know

Answer 31

just a little guide

if you have a function
f(x)=2x+4

think of it as, you start with a number
you multiply it by 2
then you add 4

so your starting number is x
you multiply it by 2
then you added 4

this gives you a new number which is represented as f(x)

so the inverse function gets you back to the original number so you do the opposite

the opposite of add 4 is subtract 4
the opposite of multiply by 2 is divide by 2

so we have

\[f^{-1}(x)=\frac{ 1 }{ 2 }(x-4)\]

it is easier if you turn your given function into a word problem so you can see what you have to do to get back to the original number
which would be your inverse function

hope this helps a little more