Question

2

Which function is the inverse of f(x) = √²-²?
O A.
B.
O c.
O D.
f¹(x) = 36x² + 2, for x ≥ 0
f¹(x) = 6x² + 2, for x ≥ 0
f¹(x) = 36x + 2, for x ≥ 0
f¹(x) = 6x² - 2, for x ≥ 0

Answer 1

`\huge\boxed{\sf f^(-1)(x)=36x^2+2}`

Explanation:

Given function:

`\displaystyle f(x)=(√(x-2) )/(6)`

Put f(x) = y.

`\displaystyle y=(√(x-2) )/(6)`

Exchange x and y.

`\displaystyle x=(√(y-2) )/(6)`

Solve for y.

`\displaystyle x=(√(y-2) )/(6)`

Multiply both sides by 6.

`\displaystyle x * 6 = √(y-2) \\\\6x = √(y-2)`

Take square root on both sides.

`(6x)^2=(√(y-2) )^2\\\\36x^2 = y - 2`

Add 2 to both sides

`36x^2+2 = y`

Put y = f⁻¹(x)

`36x^2+2=f^(-1)(x)`

OR

`f^(-1)(x)=36x^2+2\\\\\rule[225]{225}{2}`