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A
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Difficulty:
25%
(medium)
Question Stats:
76% (01:17) correct
24%
(02:15)
wrong
based on 473
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If f is the function defined by \(f(x) = x^2*(1-x)^2\) for all x, then f(1-x) =
A. f(x)
B. f(x)^2
C. 1 - f(x)
D. (1-x)*f(x)
E. f(1) - f(x)
A. f(x)
B. f(x)^2
C. 1 - f(x)
D. (1-x)*f(x)
E. f(1) - f(x)
03 Sep 2011, 09:35
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petercao
\(f(x) = x^2 (1-x)^2\)
What is \(f(1-x)\)?
Just replace x with (1-x)
\(f(1-x) = (1-x)^2 (1-(1-x))^2\)
\(f(1-x) = (1-x)^2 (x)^2\)
\(f(1-x) = (x)^2(1-x)^2 = f(x)\)
Ans: "A"
********************************
Or pick x=3; 1-x=1-3=-2
\(f(1-x)=f(-2)=(-2)^2*(1-(-2))^2=4*9=36\)
Let's check each option separately:
A. f(x)
\(f(3)=3^2*(1-3)^2=9*4=36\). Holds good. Possible answer.
B. [f(x)]^2
\((36)^2\). Ignore
C. 1 - f(x)
\(1-36=-35\). Ignore
D. (1-x) f(x)
\((1-3)(36)=36*-2=-72\). Ignore
E. f(1) - f(x)
\(1^2*(1-1)^2-36=0-36=-36\). Ignore.
Only A gave us what we got with f(1-x) i.e. f(-2).
Ans: "A"
General Discussion
