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

Answer:

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

Step-by-step explanation:

Given function:

$\displaystyle f(x)=\frac{\sqrt{x-2} }{6}$

Put f(x) = y.

$\displaystyle y=\frac{\sqrt{x-2} }{6}$

Exchange x and y.

$\displaystyle x=\frac{\sqrt{y-2} }{6}$

Solve for y.

$\displaystyle x=\frac{\sqrt{y-2} }{6}$

Multiply both sides by 6.

$\displaystyle x \times 6 = \sqrt{y-2} \\\\6x = \sqrt{y-2}$

Take square root on both sides.

$(6x)^2=(\sqrt{y-2} )^2\\\\36x^2 = y - 2$

Add 2 to both sides

$36x^2+2 = y$

Put y = f⁻¹(x)

$36x^2+2=f^{-1}(x)$

OR

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