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The function f(x) = - (x + 5) * (x + 1) shown What is the range of the function ? 10 all real numbers loss than or equal to all roal numbers less than or equal to -3 all real numbers groater or equal to 4 numbors greater than or equal to -6

1 Answer

4 votes

Given:

The function is:


f(x)=-(x+5)(x+1)

To find:

The range of the function.

Solution:

We have,


f(x)=-(x+5)(x+1)

It can be written as:


f(x)=-(x^2+x+5x+5)


f(x)=-(x^2+6x+5)

Add and subtract square of half of coefficient of x, i.e.,
\left((6)/(2)\right)^2=9.


f(x)=-(x^2+6x+9-9+5)


f(x)=-(x^2+2(x)(3)+3^2-4)


f(x)=-(x^2+2(x)(3)+3^2)+4


f(x)=-(x+3)^2+4

On comparing this equation with
f(x)=a(x-h)^2+k, we get


a=-1, it means the graph of the function is a downward parabola and the vertex is the point of maxima.


h=-3


k=4

The vertex of the function is (-3,4). So, the value of the function cannot be greater than 4.

Therefore, the range of the function is all real numbers less than or equal to 4.

Note: All options are incorrect.

User Amarnasan
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