Question

Calculus Help

Answer 1

Given \[f : x \rightarrow 5x-2\] and \[h: x \rightarrow 3x/4\] show that \[(f ^{-1} \times h ^{-1})(x)=(h \times f)^{-1}(x).\]

Answer 2

first we find the inverse for them
\[f ^{-1}(x)= \frac{ x+2 }{ 5 }\]

\[h ^{-1}(x)=\frac{ 4x }{ 3 }\]

Answer 3

are you solving for x where they are equal?? or is this supposed to be an identity...it doesn't seem to work for these functions if i am doing it right

Answer 4

\[(4x+6)/15\] is the answer but I'm not sure how to get there

Answer 5

oh i see...your notation is confusing, it should be
\[f^{-1}(h^{-1}(x)) = h(f(x))^{-1}\]

i thought we were multiplying functions,this is composition of functions

Answer 6

yea, but i'm confused about how to fill in the 'f' and 'h' part

Answer 7

no @dumbcow I was solving for y which is the function...
just I Need me a moment to think about it

Answer 8

@Ahmad1 , no issues there ....those are correct inverse functions

Answer 9

@Born_Sinner , plug "h inverse" into "f inverse" and simplify
\[\large \frac{\frac{4x}{3} +2}{5}\]

Answer 10

hmmmmm do you think that this is the indicated operation? I mean this does not seems composition to me

Answer 11

\[(f ^{-1}*h ^{-1})(x)\] ?

Answer 12

haha thats what i thought but given the answer its def composition

also identity does not work if you are using multiplication operation

Answer 13

lol is that a resume ? prob should delete that

Answer 14

yea my bad. i uploaded the wrong doc

Answer 15

lol this called composition @Born_Sinner
you can go ahead, you were so clever to realize that ;)

Answer 16

anyways we have the composite of them is what my friend @dumbcow said which is \[\frac{ \frac{ 4x }{ 3 }+2 }{ 5 }\]
just multiply by 3 to get the formula you gave us

Answer 17

still we have to prove it to the other side (h o f)(x)= \[\frac{ 3(5x-2) }{ 4 } = \frac{ 15x-6 }{ 4 }\] just find the inverse,
\[4y=15x-6 \rightarrow \frac{ 4y+6 }{ 15 }\rightarrow y=\frac{ 4x+6 }{ 15 }\]

Answer 18

still we have to prove it to the other side (h o f)(x)= \[\frac{ 3(5x-2) }{ 4 } = \frac{ 15x-6 }{ 4 }\] just find the inverse,
\[4y=15x-6 \rightarrow \frac{ 4y+6 }{ 15 }\rightarrow y=\frac{ 4x+6 }{ 15 }\]

Answer 19

I am sorry the connection went down :(