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How do I find this Inverse?? Please help!?
F(x) = x/ sqrt (x^2 +7 )
2 Answers
- NiallLv 75 years ago
Swap the x and y terms:
x = y / sqrt(y^2 + 7)
Now solve for y:
xsqrt(y^2 + 7) = y
Square both sides:
x^2(y^2 + 7) = y^2
x^2y^2 + 7x^2 = y^2
Move all the y terms to one side:
x^2y^2 - y^2 = -7x^2
Factor out y^2:
y^2(x^2 - 1) = -7x^2
Divide both sides by (x^2 - 1):
y^2 = -7x^2 / (x^2 - 1)
Without restrictions, the function could be positive or negative. So it doesn't have an inverse.
- ?Lv 65 years ago
y = x / √(x^2 + 7)
Swap x and y ,
x = y / √(y^2 + 7)
x^2 = y^2 / (y^2 + 7)
... note : y ≧ 0 ⇔ x ≧ 0 , y < 0 ⇔ x < 0 .
x^2 = (y^2 + 7) / (y^2 + 7) - 7 / (y^2 + 7)
x^2 = 1 - 7 / (y^2 + 7)
x^2 - 1 = -7 / (y^2 + 7)
y^2 + 7 = 7 / (1 - x^2)
y^2 = 7 / (1 - x^2) - 7
... See note , the answer is :
y = √[ 7 / (1 - x^2) - 7 ] if x ≧ 0
y = -√[ 7 / (1 - x^2) - 7 ] if x < 0
The domain of this function is -1 < x < 1 .
