Mathematics: Find the inverse of the function. f(x) = 7x + 8

Find the inverse of the function. f(x) = 7x + 8

Ответ:

stranger123

01.01.2022

Mathematics

The inverse of the function f(x) = 7x + 8 is $f^{-1}(x) = \frac{x}{7} - \frac{8}{7}$

The given function is:

f(x) = 7x + 8

Make x the subject of the formula:

7x = f(x) - 8

Divide through by 7

$\frac{7x}{7} = \frac{f(x)}{7} - \frac{8}{7} \\x = \frac{f(x)}{7} - \frac{8}{7} \\$

Replace x by $f^{-1}(x)$ and f(x) by x

$f^{-1}(x) = \frac{x}{7} - \frac{8}{7}$

The inverse of the function f(x) = 7x + 8 is $f^{-1}(x) = \frac{x}{7} - \frac{8}{7}$

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Ответ:

howell62

01.01.2022

Mathematics

$\frac{x-8}{7}$

Step-by-step explanation:

A way to find the inverse function is to swap the x and y (f(x)) in the equation.

$y = 7x + 8\\x = 7y + 8\\x-8 = 7y\\y = \frac{x-8}{7}$

We can check that it is an inverse function by using a property of inverse functions:

f(g(x)) = x

If we plug in the f(x) function into the variable x of the inverse function, we should end up with x

$y = \frac{(7x + 8) - 8}{7}\\y = \frac{7x}{7} \\y = x\\$

It checks out!

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Ответ:

raveransaw

23.04.2021

Mathematics

Option A is correct

Step-by-step explanation:

Correct on edge2021

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Find the inverse of the function. f(x) = 7x + 8

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