What is the range of the function $f(x)= -sqrt((x^2) -9x)$ ?

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Answer 1 · 2017-07-08T12:00:01

Range of $f(x) = (-oo, 0]$

$f(x) = -sqrt(x^2-9x)$

First let's consider the domain of $f(x)$

$f(x)$ is defined where $x^2-9x>=0$

Hence where $x<= 0$ and $x>=9$

$:.$ Domain of $f(x) = (-oo, 0] uu [9, +oo)$

Now consider:

$lim_ (x->+-oo) f(x) =-oo$

Also: $f(0)= 0$ and $f(9) = 0$

Hence the range of $f(x) = (-oo, 0]$

This can be seen by the graph of #f(x) below.

graph{-sqrt(x^2-9x) [-21.1, 24.54, -16.05, 6.74]}

Answer 2 · 2017-07-08T12:05:14

Range : $f(x) <= 0$ , in interval notation : $(-oo,0]$

$f(x) = - sqrt(x^2-9x)$

Range: Under root should be $>=0$ , So $f(x) <=0$

Range : $f(x) <= 0$ , in interval notation : $(-oo,0]$

graph{-(x^2-9x)^0.5 [-320, 320, -160, 160]} [Ans]

What is the range of the function f(x)= -sqrt((x^2) -9x) f(x)= -sqrt((x^2) -9x) ?