Answer :
[tex]\boxed{(r-s)(x)=-3x-1} \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x} \\ \\ \boxed{(r+s)(-2)=-15}[/tex]
Explanation:
In this exercise, we have the following functions:
[tex]r(x)=2x-1 \\ \\ s(x)=5x[/tex]
And they are defined for all real numbers x. So we have to write the following expressions:
First expression:
[tex](r-s)(x)[/tex]
That is, we subtract s(x) from r(x):
[tex](r-s)(x)=2x-1-5x \\ \\ Combine \ like \ terms: \\ \\ (r-s)(x)=(2x-5x)-1 \\ \\ \boxed{(r-s)(x)=-3x-1}[/tex]
Second expression:
[tex](r\cdot s)(x)[/tex]
That is, we get the product of s(x) and r(x):
[tex](r\cdot s)(x)=(2x-1)(5x) \\ \\ By \ distributive \ property: \\ \\ (r\cdot s)(x)=(2x)(5x)-(1)(5x) \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x}[/tex]
Third expression:
Here we need to evaluate:
[tex](r+s)(-2)[/tex]
First of all, we find the sum of functions r(x) and s(x):
[tex](r+s)(x)=2x-1+5x \\ \\ Combine \ like \ terms: \\ \\ (r+s)(x)=(2x+5x)-1 \\ \\ (r+s)(x)=7x-1[/tex]
Finally, substituting x = -2:
[tex](r+s)(-2)=7(-2)-1 \\ \\ (r+s)(-2)=-14-1 \\ \\ \boxed{(r+s)(-2)=-15}[/tex]
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Parabola: https://brainly.com/question/12178203
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