Question

I need help finding the inverse of the function above, 15 points.

Answer 1

`\huge\boxed{\sf f^(-1)(x)=(x)/(2) + 1}`

Explanation:

Given function:

f(x) = 2(x - 1)

Put f(x) = y

y = 2(x - 1)

Exchange x and y

x = 2(y - 1)

Now, solve for y:

x = 2(y - 1)

Divide both sides by 2

`\displaystyle (x)/(2) = y - 1`

Add 1 to both sides

`\displaystyle (x)/(2) + 1 = y`

Put y = f⁻¹(x)

`\displaystyle (x)/(2) + 1 = f^(-1)(x)`

OR

`\displaystyle f^(-1)(x)=(x)/(2) + 1 \\\\\rule[225]{225}{2}`