The inverse of given function is [tex]f^{-1}(x) = 3x-6[/tex]
Step-by-step explanation:
Given function is:
[tex]f(x) = \frac{1}{3}x+2[/tex]
In order to find the inverse, first of all we will replace the f(x) with y
[tex]y = \frac{1}{3}x+2[/tex]
Replacing x with y and y with x as the input becomes output and output becomes input in the inverse of a function
So,
[tex]x = \frac{1}{3}y+2[/tex]
Soling for y, multiplying both sides by 3 to eliminate fraction
[tex]3x = \frac{1}{3}y * 3 + 2 *3\\3x = y + 6\\3x-6 = y[/tex]
Replacing y with f^(-1)
[tex]f^{-1}(x) = 3x-6[/tex]
Hence,
The inverse of given function is [tex]f^{-1}(x) = 3x-6[/tex]
Keywords: Functions, inverse
Learn more about inverse of functions at:
- brainly.com/question/4694425
- brainly.com/question/4695279
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