Asked by Jamie Stallings on May 11, 2024
Verified
Find the inverse function of f(x) =6−xf ( x ) = 6 - xf(x) =6−x .
A) f−1(x) =6−xf ^ { - 1 } ( x ) = 6 - xf−1(x) =6−x
B) f−1(x) =−6−xf ^ { - 1 } ( x ) = - 6 - xf−1(x) =−6−x
C) f−1(x) =6f ^ { - 1 } ( x ) = 6f−1(x) =6
D) f−1(x) =6+xf ^ { - 1 } ( x ) = 6 + xf−1(x) =6+x
E) f−1(x) =−6+xf ^ { - 1 } ( x ) = - 6 + xf−1(x) =−6+x
Inverse Function
A function that reverses the operation of a given function, so that if the original function applied to an input gives a certain output, the inverse function applied to that output returns the original input.
Function
A relation between a set of inputs and a set of permissible outputs, where each input is related to exactly one output.
- Calculate and interpret the inverse of given functions.
Verified Answer
SM
Sydney McDanielsMay 13, 2024
Final Answer :
A
Explanation :
To find the inverse function, swap xxx and yyy and solve for yyy . Starting with y=6−xy = 6 - xy=6−x , swapping gives x=6−yx = 6 - yx=6−y , which rearranges to y=6−xy = 6 - xy=6−x , showing that the inverse function is the same as the original function.
Learning Objectives
- Calculate and interpret the inverse of given functions.