Inverse Function f(x)= 5 -1/3x
Mathematics · High School · Mon Jan 18 2021
Answered on
Given the function:
f(x) = 5 - ⅓x
Determine the inverse function.
Solution:
Inverse function is written in the form f^-1(x), hence to convert a function into an inverse function, we equate the value of f(x) to y, then interchange y and x, and lastly solve for x. To clearly understand this, please refer to the solution below.
f(x) = 5 - ⅓x
y = 5 - ⅓x
x = 5 - ⅓y
Transpose -⅓y and x to the opposite side of their equations, hence we must take note that in transposing a number, the sign changes.
⅓y = 5 -x
Multiply both sides by 3 in order to cancel out ⅓y.
(3) ⅓y = 5 -x (3)
y = 15 - 3x
Final answer:
f^-1(x) = 15 - 3x