Answer:
[tex]\frac{x-8}{7}[/tex]
Step-by-step explanation:
A way to find the inverse function is to swap the x and y (f(x)) in the equation.
[tex]y = 7x + 8\\x = 7y + 8\\x-8 = 7y\\y = \frac{x-8}{7}[/tex]
We can check that it is an inverse function by using a property of inverse functions:
[tex]f(g(x)) = x[/tex]
If we plug in the f(x) function into the variable x of the inverse function, we should end up with x
[tex]y = \frac{(7x + 8) - 8}{7}\\y = \frac{7x}{7} \\y = x\\[/tex]
It checks out!
The inverse of the function f(x) = 7x + 8 is [tex]f^{-1}(x) = \frac{x}{7} - \frac{8}{7}[/tex]
The given function is:
f(x) = 7x + 8
Make x the subject of the formula:
[tex]7x = f(x) - 8[/tex]
Divide through by 7
[tex]\frac{7x}{7} = \frac{f(x)}{7} - \frac{8}{7} \\x = \frac{f(x)}{7} - \frac{8}{7} \\[/tex]
Replace x by [tex]f^{-1}(x)[/tex] and f(x) by x
[tex]f^{-1}(x) = \frac{x}{7} - \frac{8}{7}[/tex]
The inverse of the function f(x) = 7x + 8 is [tex]f^{-1}(x) = \frac{x}{7} - \frac{8}{7}[/tex]
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