Question

If ,f(x)=1/4x+3 what is the equation for f–1(x)?

f–1(x) = 4x - 3


f–1(x) = 4(x - 3)


f–1(x) = 4(x + 3)


f–1(x) = 4x + 3

Answer 1

`f {}^( - 1) (x) = 4(x + 3)`

Explanation:

We would like to find the inverse of the following function .

`\longrightarrow f(x) = (1)/(4)x +3`

Step 1 : Replace
`f(x)` with
`y` . We have

`\longrightarrow y =(1)/(4)x +3`

Step 2 : Interchange x and y :-

`\longrightarrow x = (1)/(4)y + 3`

Step 3 : Solve for y :-

`\longrightarrow x - 3 =(1)/(4)y`

Multiply both sides by 4,

`\longrightarrow 4(x-3) = y`

Step 4 : Replace y with f-¹(x) :-

`\longrightarrow 4(x -3)=f^(-1)(x)`

Interchange the sides ,

`\longrightarrow \underline{\underline{ f^(-1)(x)= 4(x-3)}}{}`

And we are done !