Question

For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=4-2 √x

Answer 1

If the function f(x) = 4 - 2√x  then the inverse function be $x^{2}$ −8x+18 = f(x)

What is meant by inverse function?

An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.

Assume that the function is $f(x) = 4 + \sqrt{x-2}$ and f(x) = 4+x−2

​where the x − 2 is under the radical sign.

The first step is to swap the f(x) and x.

The new function would be

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

To solve the value of f(x) in the new function

x = 4 + $\sqrt[2]{f(x)-2}$

x - 4 = $\sqrt{f(x)-2}$

simplifying the above equation, we get

$(x -4^{} )^{2}$ = f(x) − 2

$x^{2}$ − 8x +16 = f(x) − 2

$x^{2}$ − 8x + 18 = f(x)

The inverse of the function f(x) = 4 - 2√x is $x^{2}$ −8x+18 = f(x)

To learn more about inverse function, refer to:

to brainly.com/question/25292087

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