Question

Find the inverse of the function f(x)= 2x - 4 and show explain each step used to find the inverse.

Answer 1

f-1(x)=(x+4)/2

Explanation:

y = 2x – 4

Interchange the variables:

X = 2y – 4

solve for y

2y – 4 = 2

add 4

2y – 4 + 4 = x + 4

2y = x + 4

divide each term by 2 and simplify

2y/2 2 4/2 + 4/2

Y 2 4/2 + ½

solve for y and replace it with f^-1(x)

F-1(x) 2 x/2 + ½

Answer 2

F(x) is another way of saying y
Y=2x-4

For the inverse you trade the x and y

X=2y-4
Then get y by itself
Add 4 to both sides
X+4=2y

Divide both sides by 2
X+4/2Z