Question

Function f(x)=9(x⁵+10)-7, find f^⁻¹(x)

Answer 1

To find the inverse of the function f(x) = 9(x⁵ + 10) - 7, perform algebraic manipulations to solve for x in terms of y, which involves steps such as adding 7, dividing by 9, subtracting 10, and finally taking the fifth root.

Step-by-step explanation:

To find the inverse function of f(x) = 9(x⁵ + 10) - 7, you need to solve for x in terms of y. You first replace f(x) with y to make the equation y = 9(x⁵ + 10) - 7. To solve for x, follow these steps:

1. Add 7 to both sides: y + 7 = 9(x⁵ + 10)
2. Divide both sides by 9: (y + 7) / 9 = x⁵ + 10
3. Subtract 10 from both sides: ((y + 7) / 9) - 10 = x⁵
4. Take the 5th root of both sides to solve for x. Keep in mind that there may be multiple roots, but we are typically interested in the principal root for real functions.

The inverse function, f⁻¹(x), is then given by the expression for x that we have just found.