Question

PLEASE HELP I ONLY NEED THIS ONE TO FINISH THE SECTION


The functions r and s are defined as follows.

r(x) = -2x + 1

s(x) = -x^2 + 2

Find the value of .

r(s(3))

Answer 1

Answer:

The value of r(s(3)) = -21

Step-by-step explanation:

It is given that,

r(x) = -2x + 1

s(x) = -x^2 + 2

To find the value of r(s(3))

s(x) = -x^2 + 2

s(3) = (-3)^2 + 2    [Substitute 3 instead of x]

 = 9 + 2

 = 11

Therefore s(3) = 11

r(x) = -2x + 1

r(s(3)) = r(11)   [Substitute 11 instead of x]

 =   -2(11) + 1

 = -22 + 1

  = -21

Therefore the value of r(s(3)) = -21

Answer 2

Hello!

The answer is:

$r(s(3))=15$

Why?

To solve the problem, first, we need to compose the functions, and then evaluate the obtained function. Composing function means evaluating a function into another function.

We have that:

$f(g(x))=f(x)\circ g(x)$

From the statement we know the functions:

$r(x)=-2x+1\\s(x)=-x^{2}+2$

We need to evaluate the function "s" into the function "r", so:

$r(s(x))=-2(-x^2+2)+1\\\\r(s(x))=2x^{2}-4+1=2x^{2}-3$

Now, evaluating the function, we have:

$r(s(3))=2(3)^{2}-3=2*9-2=18-3=15$

Have a nice day!