Question

What is the inverse of f(x)=−3x+5?

Answer 1

`f^(-1) (x)` =
`(-x)/(3) + (5)/(3)`

Step-by-step explanation

y = -3x +5 ---> x = -3y + 5 -> y =
`(x - 5)/(-3)`

Answer 2

f-¹(x) = (4- x)/ 3

Explanation:

inverse of a function is nothing but the value of x in terms of f(x)

like

if we write f(x) as y we'd get

y = - 3x + 5

so, ill express x in terms of y:-

y= -3x + 4

• adding 3x on both sides of the equation

y + 3x = -3x + 3x + 4

• subtracting y on both sides

y - y + 3x = 4 - y

3x = 4 - y

• dividing the whole equation by 3

x = (4 - y)/ 3

soo, the inverse of the function is x = (4- y)/ 3

mostly we write the inverse in terms of x, hey! don't get confused, when i say this, I simply mean that we're gonna replace y with x and x with f-¹(x).

therefore,

f-¹(x) = (4- x)/ 3