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melamori03 [73]
1 year ago
9

Suppose that the functions p and q are defined as follows.p(x) = -2x + 1q(x)=-x?Find the following.

Mathematics
1 answer:
MariettaO [177]1 year ago
6 0

First let us find

(q\mathrm{}p)(x)\begin{gathered} q(p(x))=q(-2x+1) \\ =-(-2x+1)^2 \\ So\text{ } \\ (q\mathrm{}p)(5)=-(-2\times5+1)^2 \\ =-(9)^2 \\ =-81 \end{gathered}

Now let;s solve the second part

\begin{gathered} (p\mathrm{}q)(x)=p(q(x)) \\ =p(-x^2) \\ =-2(-x^2)+1 \\ =2x^2+1 \\ So\text{ (p.q)(5) will be } \\ (p\mathrm{}q)(5)=2(5)^2+1 \\ =51 \end{gathered}

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The distance between two points with the given coordinates in space is;

<u><em>Distance = 17 units</em></u>

We are given the coordinates;

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d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

From the equation given to us, we can see that;

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