a)The functions f and g are defined by f(x) = root x for x > 0; g(x) = x - 1 for all values of x.

i.)Write down expressions for fg(x) and gf(x).

> fg(x) = root x - 1

> gf(x) = root x - 1

ii.) Verify that x = 1 => fg(x) = gf(x)

>??????

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- Jun 27th 2010, 03:43 PMansonboundVerify that x = 1 => fg(x) = gf(x)
a)The functions f and g are defined by f(x) = root x for x > 0; g(x) = x - 1 for all values of x.

i.)Write down expressions for fg(x) and gf(x).

> fg(x) = root x - 1

> gf(x) = root x - 1

ii.) Verify that x = 1 => fg(x) = gf(x)

>?????? - Jun 27th 2010, 04:15 PMskeeter
$\displaystyle f(x) = \sqrt{x}$ , $\displaystyle x > 0$

$\displaystyle g(x) = x - 1$

I assume you mean function composition by the notation "fg(x) and gf(x)"

$\displaystyle f[g(x)] = f(x-1) = \sqrt{x-1}$

$\displaystyle g[f(x)] = g(\sqrt{x}) = \sqrt{x} - 1$

you should be able to see that $\displaystyle f[g(1)] = g[f(1)] = 0$ - Jun 27th 2010, 04:20 PMansonbound
- Jun 27th 2010, 04:30 PMskeeter
- Jun 27th 2010, 04:58 PMansonbound
the last question..

http://farm5.static.flickr.com/4074/...9568b56a_b.jpg - Jun 27th 2010, 05:04 PMskeeter
$\displaystyle y = \sqrt{x-1}$

swap variables ...

$\displaystyle x = \sqrt{y-1}$

solve for y to finish - Jun 27th 2010, 05:53 PMansonbound
- Jun 27th 2010, 06:02 PMansonbound
- Jun 27th 2010, 06:05 PMskeeter
sketch the graph y = |2x-4|

sketch the graph y = x

how far up will you have to translate y = |2x-4| so that it touches y = x at only one point?