Question

Find the inverses for f(x)=9x^2-7

Answer 1

To find the inverses of the function f(x) = 9x^2 - 7, add 7 to both sides, divide by 9, and take the square root of both sides, remembering to consider both positive and negative roots.

Step-by-step explanation:

To find the inverses of the function f(x) = 9x^2 - 7, we must solve for x in terms of y. Since y = f(x), we can write y = 9x^2 - 7. To find x, we'll perform the following steps:

1. Add 7 to both sides of the equation: y + 7 = 9x^2.
2. Divide both sides by 9: (y + 7) / 9 = x^2.
3. Take the square root of both sides to solve for x: x = ±√((y + 7) / 9). Because we have a quadratic function, there will be two solutions for x, one with a positive square root and one with a negative square root.

The solutions represent the inverses of the given function.