Find the inverse of the given one-to-one function f. f(x)=(x-4)/(2x+1)

hexacordoK

hexacordoK

Answered question

2021-05-17

Find the inverse of the given one-to-one function f. f(x)=x42x+1

Answer & Explanation

Laaibah Pitt

Laaibah Pitt

Skilled2021-05-18Added 98 answers

Let y=f(x): y=x42x+1
Swap the variables: x=y42y+1
Solve for y. Multiply both sides by 2y+1:x(2y+1)=y4
2xy+x=y4
Add 4 to both sides: 2xy+x+4=y
Subtract 2cy from both sides: x+4=y2xy
Factor out y: x+4=y(12x)
Divide both sides by 1 — 2x: x+412x=y
or
y=x+42x1
The new y is the inverse of f: f1(x)=x+42x1

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