Question

F(x)=x^7/9

Show the work steps of the function above to find the inverse of the function algebraically using rational exponents notation. Do not use radical notation.

Answer 1

To find the inverse function of f(x) = x^7/9, replace f(x) with y, and then raise both sides to the power of 9/7 to isolate x. The resulting inverse function is f^-1(x) = x^9/7. We confirm the inverse by checking that compositions f(f^-1(x)) and f^-1(f(x)) yield x.

Step-by-step explanation:

To find the inverse of the function f(x) = x7/9, we perform algebraic operations to solve for x in terms of y.

1. First, replace f(x) with y to get y = x7/9.
2. Next, raise both sides to the reciprocal power to isolate x, resulting in x = y9/7.
3. The left side now reads as x = f-1(y) where f-1 is the inverse function.

Therefore, the inverse function is f-1(x) = x9/7.

We check that the inverse is correct by confirming that f(f-1(x)) = x and f-1(f(x)) = x which demonstrates that f and f-1 are indeed inverses.

Answer 2

x^(9/7)

Step-by-step explanation:

inverse function f(x) = (x^(1/9))^7 = x^(9/7)