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A couple of Functions questions

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A couple of Functions questions [#permalink] New post 27 Aug 2009, 03:50
:arrow: If f(x) is defined as the greatest integer less than \frac{x}{7}, and g(x) is defined as the least integer greater than \frac{x}{7}, then what is the value of f(115) + g(60)?

:arrow: If f(x) = x^2 - 7x - 10 and g(x) = f(x-7), what is the positive root of the equation f(x) = g(2)?

:gl
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Re: A couple of Functions questions [#permalink] New post 27 Aug 2009, 06:53
1)
f(115) = 115/7 = 16(3/7) = 16
g(60) = 8(4/7) = 9
So f(115) + g(60) = 25

2) f(x) = x^2 - 7x - 10
g(x) = f(x-7)
f(x) = g(2)
g(2) = f(2-7) = f(-5) = 25 + 35 - 10 = 50
Square root (50) = 5 * square root(2)
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Re: A couple of Functions questions [#permalink] New post 28 Aug 2009, 02:45
Hi Aleehsgonji, you solved nicely the first, however you misread 'positive root' as 'positive square root'.

f(x) = g(2) = 50

x^2 - 7x - 60 = 0

(x+5)(x-12)

Therefore, the positive root is 12.
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Re: A couple of Functions questions   [#permalink] 28 Aug 2009, 02:45
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