Asked by rachel
Find a formula for the inverse of the function
f(x)=9−4/x2, x>0.
f(x)=9−4/x2, x>0.
Answers
Answered by
Reiny
original:
y = 9 - 4/x^2
inverse:
x = 9 - 4/y^2
solving that for y:
xy^2 = 9y^2 - 4
xy^2 - 9y^2 = -4
y^2(x -9) = -4
y^2 = -4/(x-9)
y^2 = 4/(9-x)
y = ± √(9-x)
the new equation is NOT a function
y = 9 - 4/x^2
inverse:
x = 9 - 4/y^2
solving that for y:
xy^2 = 9y^2 - 4
xy^2 - 9y^2 = -4
y^2(x -9) = -4
y^2 = -4/(x-9)
y^2 = 4/(9-x)
y = ± √(9-x)
the new equation is NOT a function