Question

The inverse of F(x) is a function. True or false ?

Answer 1

True just did the test

Answer 2

The answer is True

Explanation:

we know that

The function f(x) is a vertical parabola open downward

so

The equation of f(x) into vertex form is equal to

`f(x)=-a(x-h)^(2)+k`

where

(h,k) is the vertex of the parabola

Let

`y=f(x)`

`y=-a(x-h)^(2)+k`

Exchanges the variables x for y and y for x

`x=-a(y-h)^(2)+k`

Isolate the variable y

`x-k=-a(y-h)^(2)`

the coefficient a is negative

`(x-k)/(-a)=(y-h)^(2)`

`(k-x)/a=(y-h)^(2)`

`y=(+/-)√((k-x)/a)+h`

Let

`f^(-1)(x)=y`

`f^(-1)(x)=(+/-)√((k-x)/a)+h` ------> inverse of the function f(x)

therefore

The inverse of f(x) is a function