Can't think of an easier way but to plug in the function values in each.
Lets start with (E)
f(x) = -3x => f(a) = -3a and f(b) = -3b
f(a+b) = -3(a+b) = -3a -3b = f(a) + f(b)
Hence, [spoiler](E) is correct[/spoiler]
PS3
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Rahul@gurome
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Let's check each of the options one by one.winter wrote:For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
1) f(x) = x square
2) f(x) = x + 1
3) f(x) = underroot x
4) f(x) = 2/x
5) f(x) = -3x
(1) f(a+b) = (a+b)^2 = a^2 + 2ab + b^2. But f(a) + f(b) = a^2 + b^2. So (1) is not true.
(2) f(a + b) = (a+b +1). But f(a) + f(b) = a+1 + b+1 = a+b+2. So (2) is not true.
(3) f(a+b) = √(a+b). But f(a) + f(b) = √a + √b. So (3) is not true.
(4) f(a+b) = 2/(a+b). But f(a) + f(b) = 2/a + 2/b = 2(a+b)/ab. So (4) is not true.
(5) f(a+b) = -3(a+b). But f(a) + f(b) = -3a - 3b = -3(a +b) = f(a+b). Hence, (5) is true.
The correct answer is (5).
Rahul Lakhani
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sumanr84
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These are generally added in the test as Time Busters as we need to check for all options. Start either from Middle or Last. I prefer from Last.winter wrote:For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
1) f(x) = x square
2) f(x) = x + 1
3) f(x) = underroot x
4) f(x) = 2/x
5) f(x) = -3x
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Rahul@gurome
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You are correct!sumanr84 wrote: These are generally added in the test as Time Busters as we need to check for all options. Start either from Middle or Last. I prefer from Last.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
