Answer :
[tex]f(x)=9x+7\\
y=9x+7\\
9x=y-7\\
x=\dfrac{1}{9}y-\dfrac{7}{9}\\
f^{-1}(x)=\dfrac{1}{9}x-\dfrac{7}{9}\\[/tex]
Applying it's definition, the inverse of the function f(x) = 9x + 7 is given by:
[tex]f^{-1}(x) = \frac{x - 7}{9}[/tex]
How to find the inverse of a function?
Suppose we have a function y = f(x). To find the inverse function, we exchange x and y in the original function, then isolate f.
In this problem, the function is:
y = 9x + 7
Exchanging:
x = 9y + 7
Isolating y:
9y = x - 7
[tex]y = \frac{x - 7}{9}[/tex]
[tex]f^{-1}(x) = \frac{x - 7}{9}[/tex]
More can be learned about inverse functions at https://brainly.com/question/8824268
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