Question

Determine the inverse of the function f (x) = 4(x − 3)2 + 2. inverse of f of x is equal to 3 minus the square root of the quantity x over 4 minus 2 end quantity such that the domain of f (x) is x ≤ 3 inverse of f of x is equal to 3 minus the square root of the quantity x over 4 minus 2 end quantity such that the domain of f (x) is x ≥ 3 inverse of f of x is equal to 3 minus the square root of the quantity of the quantity x minus 2 end quantity over 4 end quantity such that the domain of f (x) is x ≤ 3 inverse of f of x is equal to 3 minus the square root of the quantity of the quantity x minus 2 end quantity over 4 end quantity suchsuch that the domain of f (x) is x ≥ 3

Answer 1

The inverse of the function f(x)  = 4(x-3)² + 2 is $f^{-1}(x) = \sqrt{\frac{x-2}{4} } + 3$

The given function is:

f(x)   =  4(x  - 3)²  +  2

To find the inverse of the function:

Make x as the subject of the formula

$4(x-3)^2 = f(x) - 2\\(x-3)^2 = \frac{f(x)-2}{4} \\x - 3 = \sqrt{\frac{f(x)-2}{4} } \\x = \sqrt{\frac{f(x)-2}{4} } + 3$

Replace x by $f^{-1}(x)$ and replace f(x) by x

$f^{-1}(x) = \sqrt{\frac{x-2}{4} } + 3$

Therefore, the inverse of the function is:

$f^{-1}(x) = \sqrt{\frac{x-2}{4} } + 3$

Learn more here: brainly.com/question/17285960