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

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Adetunmbiadekunle Adetunmbiadekunle · Answer 1 · 2021-10-01T12:35:07+02:00

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

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

[tex]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[/tex]

Replace x by [tex]f^{-1}(x)[/tex] and replace f(x) by x

[tex]f^{-1}(x) = \sqrt{\frac{x-2}{4} } + 3[/tex]

Therefore, the inverse of the function is:

[tex]f^{-1}(x) = \sqrt{\frac{x-2}{4} } + 3[/tex]

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