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Which equation is the inverse of y = 9x^2 – 4?
Answer: y = ± [ √(x+4) ] / 3
Solution:
1) To find the inverse of the function y = 9x^{2} – 4, exchange the variables x and y, and then solve for the new y.
2) Exchange of the variables: y = 9x^{2} – 4 → x = 9y^{2} – 4
3) Solve for y:
=> 9y^{2} = x + 4
=> y^{2} = [x + 4] / 9
=> y = ± [ √(x + 4) ] / 3