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
[tex]f(x)=-a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
Let
[tex]y=f(x)[/tex]
[tex]y=-a(x-h)^{2}+k[/tex]
Exchanges the variables x for y and y for x
[tex]x=-a(y-h)^{2}+k[/tex]
Isolate the variable y
[tex]x-k=-a(y-h)^{2}[/tex]
the coefficient a is negative
[tex](x-k)/(-a)=(y-h)^{2}[/tex]
[tex](k-x)/a=(y-h)^{2}[/tex]
[tex]y=(+/-)\sqrt{(k-x)/a}+h[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=(+/-)\sqrt{(k-x)/a}+h[/tex] ------> inverse of the function f(x)
therefore
The inverse of f(x) is a function
