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Original Question
If f(x)= Sqrt 2+5x find f^-1.Asked by Dillan
If f(x)= Sqrt(2+5x) find f^-1.
Answers
Answered by
Reiny
let y = √(2+5x) for all x ≥ -2/5
the inverse is
x = √(2+5y)
x^2 = 2+5y
5y = x^2 - 2
y = (x^2 - 2)/5
test: in original, let x = 4
y = √(2 + 20) = √22
in inverse: let x = √22
y = (√22^2 - 2)/5 = 20/5 = 4
f^-1 = (x^2 - 1)/5
the inverse is
x = √(2+5y)
x^2 = 2+5y
5y = x^2 - 2
y = (x^2 - 2)/5
test: in original, let x = 4
y = √(2 + 20) = √22
in inverse: let x = √22
y = (√22^2 - 2)/5 = 20/5 = 4
f^-1 = (x^2 - 1)/5
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