Find the inverse of the one-to-one function.
http://awesomescreenshot.com/00c32rka6d

I think the answer is
$$f ^{1}(x)=$$
$$\frac{ 7 }{ 2x+5 }$$

Question

Find the inverse of the one-to-one function.
http://awesomescreenshot.com/00c32rka6d

I think the answer is
$$f ^{1}(x)=$$
$$\frac{ 7 }{ 2x+5 }$$

ganeshie8 · Answer

thats a very good wrong guess :)

ganeshie8 · Answer

what do you call in writing when you use the same word to convey two different meanings ?

anonymous · Answer

>.< ummmm synonym?

anonymous · Answer

wait wait

anonymous · Answer

ummmm homonyms?

ganeshie8 · Answer

i think so...  so same here, the word inverse means two different things :
1) multiplicative inverse of a number 2 is  1/2
2) inverse of a function is a different concept.

ganeshie8 · Answer

here is the method to find the inverse of a function :
1) solve for x
2) replace x and y

ganeshie8 · Answer

$\large y = f(x) = \dfrac{2x+5}{7}$

ganeshie8 · Answer

1) solve for x :

$\large y = \dfrac{2x+5}{7}$

$\large 7y = 2x+5 $

$\large 7y-5 = 2x $


$\large x = \dfrac{7y-5}{2}$

ganeshie8 · Answer

2) replace x and y :

$\large y = \dfrac{7x-5}{2}$

ganeshie8 · Answer

thats your inverse function ^

anonymous · Answer

Where did the y come from? http://awesomescreenshot.com/0b332rp13d and in these answer choices where does that exponent come from?

kmeis002 · Answer

The notation $$f^{-1} (x) $$ just means that you are finding the inverse function which means it maps the range of f(x) to its domain. Its simply notation that can be confused with the reciprocal of a function, but it is not. The y is just another name for the range of the function, or f(x).

anonymous · Answer

Ooooh I understand.
Thank you both ^-^