Question

Which function is the inverse of f(x) = –5x – 4?

Answer 1

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

Answer 2

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

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