Find f(x) ,given f^-1= x^4+2x^2+3x+2?
回答 (5)
2018-11-21 4:34 pm
f⁻¹(x) = x⁴ + 2x² + 3x + 2
→ x⁴ + 2x² + 3x + 2
f⁻¹(x) = y
→ x = f(y)
f(y) = y⁴ + 2y² + 3y + 2
f(x) = x⁴ + 2x² + 3x + 2.
→ x⁴ + 2x² + 3x + 2
f⁻¹(x) = y
→ x = f(y)
f(y) = y⁴ + 2y² + 3y + 2
f(x) = x⁴ + 2x² + 3x + 2.
2018-11-21 11:22 am
2018-11-21 6:47 am
f is not a function because f^-1 is not 1-to-1 (i.e. it falls the horizontal line test) because, for example f(-1) = f(0) = 2, moreover, since the x⁴ term comes to dominate when |x| gets large, for all sufficiently large y there will be a < 0 < b such that f(a) = f(b) = y.
2018-11-21 6:39 am
y = f(x)
with
y^4 + 2y² + 3 y + 2 = x
with
y^4 + 2y² + 3 y + 2 = x
2018-11-21 6:27 am
so solve y^4 + 2y² + 3 y + 2 = x for the variable y...good luck
收錄日期: 2021-04-24 01:10:51
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