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Functions

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Source: — Problem Solving |

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by Brent@GMATPrepNow » Mon Apr 06, 2015 7:02 am
f(x) = x³ - x, g(x) = xº, h(x) = 3000x
What is h(g(f(11,254)))?

A) 0
B) 1
C) 3000
D) 379,957,548,000
E) No solution
Start from the innermost function and work our way outwards.

f(11,254) = 11,254³ - 11,254
= some big number [which we don't need to actually calculate]

g(some big number) = (some big number)º
= 1

h(1) = 3000(1)
= 3000

Answer: C

NOTE: I noted that we need not calculate f(11,254), because we end up taking the result and raising it to the power of 0, which will end up equaling 1.

Cheers,
Brent
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by mallika hunsur » Mon Apr 06, 2015 7:08 am
Brent@GMATPrepNow wrote:
f(x) = x³ - x, g(x) = xº, h(x) = 3000x
What is h(g(f(11,254)))?

A) 0
B) 1
C) 3000
D) 379,957,548,000
E) No solution
Start from the innermost function and work our way outwards.

f(11,254) = 11,254³ - 11,254
= some big number [which we don't need to actually calculate]

g(some big number) = (some big number)º
= 1

h(1) = 3000(1)
= 3000

Answer: C

NOTE: I noted that we need not calculate f(11,254), because we end up taking the result and raising it to the power of 0, which will end up equaling 1.

Cheers,
Brent
Thanks Brent, i thought the Q said f(x)=(x^3-x)g(x)=...thought they were all multiplied in a line.

Thanks again!!
Mallika
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by Brent@GMATPrepNow » Mon Apr 06, 2015 7:15 am
mallika hunsur wrote: Thanks Brent, i thought the Q said f(x)=(x^3-x)g(x)=...thought they were all multiplied in a line.

Thanks again!!
Mallika
These nested functions are treated in the same way that we'd treat nested brackets.
For example, to evaluate 10(7 + (5 + (1 + 2))), we'd start with the innermost brackets and add 1+2
Then we'd add 5 to that sum, etc.

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Brent
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by GMATGuruNY » Mon Apr 06, 2015 7:16 am
f(x) = x³ - x = x(x²-1) = (x)(x+1)(x-1).
g(x) = x�.
h(x) = 3000x.

What is the value of h ( g (f(11,254 ) ) )?
Work from the INSIDE OUT.

h ( g ( f(11,254) ) ).
First calculate the value in red.
Since f(x) = (x)(x+1)(x-1), f(11,254) = (11,254)(11,255)(11,253).

Substituting (11,254)(11,255)(11,253) for the value in red, we get:
h ( g(11,254*11,255*11,253) ).
Now calculate the value in blue.
Since g(x) = x�, g[(11,254)(11,255)(11,253)] = [(11,254)(11,255)(11,253)]� = 1.

Substituting 1 for the value in blue, we get:
h(1).
Since h(x) = 3000x, h(1) = 3000*1 = 3000.

The correct answer is C.
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