A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
For which of the following functions f is f(x) = f(1 - x) for all x?
(i) f(x)= 1-x
(ii) f(x)= 1-x2
(iii) f(x)= x2-(1-x)2
(iv) f(x)= x2(1-x)2
(v) f(x)= x/(1-x)
Solution:
Given function f(x) = f(1 – x)
By inspection,
(i) Consider f(x) = (1-x) then f(1-x) = 1-(1-x)
= x ≠ f(x)
(ii) Consider f(x) = 1-x2 then f(1-x) = 1-(1-x)2
= 1-1+2x-x2
= 2x-x2 ≠ f(x)
(iii) Consider f(x)= x2-(1-x)2 then f(1-x)
= (1-x)2 - [1-(1-x)]2
= 1-2x+x2-x2
= 1-2x ≠ f(x)
(iv) Consider f(x)= x2(1-x)2 then f(1-x)
= (1-x)2 [1 - (1-x)]2 = (1-x)2x2 = f(x)
(v) Consider f(x)= x/(1-x) then f(1-x)
= (1-x)/(1-(1-x))
= (1-x)/x ≠ f(x)
For which of the following functions f is f(x) = f(1 - x) for all x?
(i) f(x)= 1-x
(ii) f(x)= 1-x2
(iii) f(x)= x2-(1-x)2
(iv) f(x)= x2(1-x)2
(v) f(x)= x/(1-x)
Summary:
For the given function f(x)= x2(1-x)2, f(x) = f(1 – x) for all x.
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