Question

Find the inverse function

f(x)=3x-1

f^-1 (x)=x+[?]/[ ]

Answer 1

Answer :
`\bf (x+1)/(3)`

A function is given to us and we need to find out the inverse of the function . The given function is ,

`\rm \implies f(x) = 3x - 1`

Step 1: Substitute y = f(x) :-

`\rm \implies y = 3x -1`

Step 2: Interchange x and y :-

`\rm \implies x = 3y - 1`

Step 3: Solve for y :-

`\rm \implies 3y = x + 1 \\`

`\rm \implies y =(x+1)/(3)`

Step 4: Replace y with f-¹(x) :-

`\rm \implies \underline{\boxed{\red{\rm f^(-1)(x) = (x+1)/(3)}}}`

Hence the inverse of the function is (x+1)/3.

I hope this helps .