Simplify.
f^-1g^-1

a. f/g
b. g/f
c. 1/fg
d. fg

Question

Simplify.
f^-1g^-1

a. f/g 
b. g/f
c. 1/fg
d. fg

johnweldon1993 · Answer

well f^-1 would be written as
$$\frac{ 1 }{ f }$$

g^-1 would be written as
$$\frac{ 1 }{ g }$$

so together you have

$$\frac{ 1 }{ f } * \frac{ 1 }{ g }$$

which is?

anonymous · Answer

fg?

johnweldon1993 · Answer

$$\frac{ 1 * 1 }{ f * g }$$

jhannybean · Answer

f and g are two separate functions i believe

anonymous · Answer

1/fg idk im so confused

jhannybean · Answer

what are you confused about?

johnweldon1993 · Answer

1/fg would be what I get yes.....but @Jhannybean what'd you mean by that? lol

anonymous · Answer

i dont understand how f^-1 went to 1/f 
and how g^-1 went to 1/g

johnweldon1993 · Answer

ahh okay.....this is what happens when you want to turn a negative power ^-1 

into a positive power ^1

what you do...is you put the function under a fraction under 1

a.k.a

$$f ^{-1} = \frac{ 1 }{ f }$$

*because no one likes working with negative exponents....so we turn them positive by doing this

anonymous · Answer

oh ok i think i get it now ok so for example if i have y^-3 it would be 3/y ???

johnweldon1993 · Answer

not quite.....the function would STILL be under 1....

$$y ^{-3} = \frac{ 1 }{ y^3 }$$

the exponent follows the 'y'....but just becomes positive

johnweldon1993 · Answer

hmmm....another way of looking at it....you know what a reciprocal is correct?

anonymous · Answer

yes

johnweldon1993 · Answer

perfect.....you know it is just the fraction flipped upside down

$$\frac{ 1 }{ 2 } reciprocal = \frac{ 2 }{ 1 }$$

like that

well...when you have a function...raised to a negative power....a.k.a your

$$f^{-1}$$

look at the reciprocal of 'f' ...instead of 'f' it would be

$$\frac{ 1 }{ f }$$

and just bring the exponent with the 'f'

$$f^{-1} = \frac{ 1 }{ f^1 } = \frac{ 1 }{ f }$$

better?

anonymous · Answer

a little better, yes

johnweldon1993 · Answer

now let me test you

$$f^{-5} = ?$$

anonymous · Answer

1/f^5

johnweldon1993 · Answer

perfect! :)

anonymous · Answer

yay

johnweldon1993 · Answer

so now back to the original question...do you see why the answer would be
$$\frac{ 1 }{ fg }$$

anonymous · Answer

because f^-1 is 1/f and g^-1 is 1/g

johnweldon1993 · Answer

right....and then when you multiply them you get the 1/fg :)

anonymous · Answer

thank u for your help :D

johnweldon1993 · Answer

anytime! :)