givin the fuction if f(x)=3x-4/5 which of the below expressions are correct?
f−1(x) = The quantity of 5x plus 4, divided by 3.
f−1(x) = The quantity of 5x minus 4, divided by 3.
f−1(x) = The quantity of negative 3x minus 4, divided by 5.
f−1(x) = The quantity of 4 minus 3x, divided by 5.

Question

givin the fuction if f(x)=3x-4/5 which of the below expressions are correct?
 f−1(x) = The quantity of 5x plus 4, divided by 3.
 f−1(x) = The quantity of 5x minus 4, divided by 3.
 f−1(x) = The quantity of negative 3x minus 4, divided by 5.
 f−1(x) = The quantity of 4 minus 3x, divided by 5.

anonymous · Answer

@johnweldon1993

johnweldon1993 · Answer

Okay so this in inverse functions

is this

$$\large f(x) = 3x - \frac{4}{5}$$
or
$$\large f(x) = \frac{3x - 4}{5}$$

anonymous · Answer

okayy

johnweldon1993 · Answer

There was a question in that :P

anonymous · Answer

ohh my bad lol its the bottom one sorry

johnweldon1993 · Answer

Lol

alright so we have

$$\large y = \frac{3x - 4}{5}$$

Im sure you know that f(x) can just be written as 'y' right?

anonymous · Answer

yes sir :)

johnweldon1993 · Answer

Good..so yes we have

$$\large y = \frac{3x - 4}{5}$$

what the basic idea of inverse function is...you switch the 'x' ad the 'y'....then you solve again for 'y'

so...lets switch x and y
$$\large x = \frac{3y - 4}{5}$$

johnweldon1993 · Answer

And now we just need to use algebra to solve this for 'y' again...how would we do that?

anonymous · Answer

multiply the x by 5 nd 3y-4 by 5?

johnweldon1993 · Answer

Correct....leaving us with

$$\large 5x = 3y - 4$$

correct?

anonymous · Answer

yeppers

johnweldon1993 · Answer

What next? we need 'y' all by itself

anonymous · Answer

divide all of the numbers by 3 or is it just 5/3

johnweldon1993 · Answer

Hmm...well yeah we could do that first....but maybe we should add 4 to both sides first ...what do ya think?

anonymous · Answer

suree which ever way is easier for me lol

anonymous · Answer

you would get 8x = 3y right ?

johnweldon1993 · Answer

Well we COULD do it either way...lol

but now you've forced me to show you both ways :P

anonymous · Answer

nahh just do anyone idc and i didnt force you :p

johnweldon1993 · Answer

Lol :P

alright well we'll do it the other way I said

$$\large 5x = 3y - 4$$

after you add 4 to both sides you get

$$\large 5x + 4 = 3y$$

right?

anonymous · Answer

yaa

johnweldon1993 · Answer

And finally you would divide everything by 3 to solve for 'y'

$$\large f^{-1}(x) = \frac{5x + 4}{3}$$

anonymous · Answer

Omg i love you forever jk u are amazing

johnweldon1993 · Answer

Lol <3 haha glad to help :)

anonymous · Answer

can i tag u if i have anymore questions please u make me feel not stupid

johnweldon1993 · Answer

Of course :)

anonymous · Answer

thankss