Verified Answer :

Answer:

\(f^{-1}(x)=-\frac{1}{5}(x+4)\)

Step-by-step explanation:

The given function is \(f(x)=-5x-4\)

Substitute y = f(x)

\(y=-5x-4\)

Interchange x and y

\(x=-5y-4\)

Solve for y

\(x+4=-5y\\\\y=-\frac{1}{5}(x+4)\)

This is nothing but the inverse of the function. Hence,

\(f^{-1}(x)=-\frac{1}{5}(x+4)\)

The inverse of the function is \(f^{-1}(x)=-\frac{1}{5}(x+4)\)

abidemiokin

Functions are written in terms of variable. The inverse of the function f(x) = –5x – 4 is y = (x + 4)/-5

How to find the inverse of a function?

Functions are written in terms of variable. Given the function as shown:

f(x) = –5x – 4

This can be written as

y = –5x – 4

Replace y with x

x = -5y - 4

Make y the subject of the formula

-5y = x + 4

y = (x + 4)/-5

Hence the inverse of the function f(x) = –5x – 4 is y = (x + 4)/-5

Learn more on inverse of a function here: https://brainly.com/question/2873333

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