if f(x)+2f(1-x)=X^2+1 what is range
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Answered by
28
Answer:
[-1/3, ∞)
Step-by-step explanation:
Given that f(x) + 2f(1 - x) = x² + 1-----(1)
On replacing x by 1 - x, we get
f(1 - x) + 2f(x) = (1-x)² + 1 = x² -2x + 2
=>2f(1-x) + 4f(x) = 2x² - 4x + 4---(2)
Subtracting (1) from (2), we get
3f(x) = x² - 4x + 3
=> f(x) = (x² - 4x + 3)/3.
= 1/3[ (x -2)² - 1]
We will get the minimum when x = 2 i.e., -1/3
and maximum is ∞.
Thus, the range of f(x) is [-1/3, ∞).
Hope, it helped !
Answered by
2
Answer:
Step-by-step explanation:
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