Question

Find a simple transformation for all points except those indicated: f(x)=(radical(x))-1/radical(x) / 1-(1/radical(x)); g(x)=radicalx; x=0,1

Answer 1

\[f(x)=\frac{\frac{\sqrt{x}-1}{\sqrt{x}}}{1-\frac{1}{\sqrt{x}}}\]

Answer 2

like that???

Answer 3

ah no

Answer 4

radcialx then minus 1/radicalx. denominator is good though

Answer 5

\[f(x)=\frac{\sqrt{x}-\frac{1}{\sqrt{x}}}{1-\frac{1}{\sqrt{x}}}\]

Answer 6

yesss

Answer 7

ok lets multiply top and bottom by
\[\sqrt{x}\]

Answer 8

\[f(x)=\frac{x-1}{\sqrt{x}-1}\]

Answer 9

this is good at 0 because you get
\[f(0)=1\]

Answer 10

but it is still not good at 1 because you get 0/0 so now lets rationalize the denominator by multiplying top and bottom by
\[\sqrt{x}+1\]

Answer 11

quick question howd u know to rationalize the function with radical x+1?

Answer 12

\[\frac{x-1}{\sqrt{x}-1}\times \frac{\sqrt{x}+1}{\sqrt{x}+1}\]
\[\frac{(x-1)(\sqrt{x}+1)}{x-1}=\sqrt{x}+1\]

Answer 13

how do i know it? good question. but it is the same way you always rationalize a denominator or numerator. multiply by the "conjugate"

Answer 14

it works because
\[(a+b)(a-b)=a^2-b^2\]

Answer 15

oooh ok

Answer 16

so how does that equation simplify into 1+radicalx?

Answer 17

ohw wait i think i see it!

Answer 18

cancel the x - 1 top and bottom

Answer 19

thank you so much!

Answer 20

yw