Q:

Given f(x)=7x^9 , find f^1(x). Then state whether f^1f(x) is a function. a : y=(x/7)^1/9 ; f^1(x) is a function.b : y=(x/7)^9 ; f^1(x) is not a functionc : y=(x/7)^1/9 ; f^1(x) is not a functiond : y=(x/7)^9 ; f^1(x) is a function

Accepted Solution

A:
Answer:A though without graphing software it would appear to be CStep-by-step explanation:The inverse of a function is the function reflected across the line y=x. This results in the coordinate points (x,y) of the function becoming (y,x) for the inverse function. Algebraically to find the inverse, switch the x and y locations and solve for y.y = 7x^9x = 7y^9x/7 = y^9(9)√(x/7) = yThis is a ninth root of (x/7) also written in exponents as y = (x/7)^(1/9).This is a function. While it appears not to be a function because the middle portion over the origin appears vertical, it is a function because the middle portion over the origin is changing and graphing software shows it has no input with more than one output. Without graphing software you would rule it is not a function.