Question

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

Answer 1

True just did the test

Answer 2

Answer:

The answer is True

Step-by-step 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

$(x-k)/(-a)=(y-h)^{2}$

$(k-x)/a=(y-h)^{2}$

$y=(+/-)\sqrt{(k-x)/a}+h$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=(+/-)\sqrt{(k-x)/a}+h$ ------> inverse of the function f(x)

therefore

The inverse of f(x) is a function