Question

Suppose that the functions p and q are defined as follows.

Answer 1

The most appropriate choice for function can be given by

q$o$p(3) =  $\sqrt{15}+1$

p$o$q(3) =  $2\sqrt{3} + 10$

What is function?

A function from A to B is a rule that maps to each element of A a unique element of B.

A is called the domain of the function and B is called the co domain of the function.

We can do addition, subtraction, multiplication, division and composition on functions.

Let f and g be two functions

f$o$g(x) = f(g(x)) and g$o$f(x) = g(f(x))

This is known as composition of function.

Here,

$p(x) = x^2 + 6\\q(x) = \sqrt{x} +1$

q$o$p(x) = q(p(x))

          =$q(x^2+6)$

          = $\sqrt{x^2+6}+1$

q$o$p(3) = $\sqrt{3^2+6}+1$

          = $\sqrt{15}+1$

p$o$q(x) = p(q(x))

          = p($\sqrt{x}+1$)

          = $(\sqrt{x}+1)^2+6$

          = $x + 1 + 2\sqrt{x} + 6$

          = $x + 2\sqrt{x} +7$

p$o$q(3) = $3 + 2\sqrt{3} +7$

               $2\sqrt{3} + 10$

               $2\sqrt{3} + 10$

To learn more about functions, refer to the link:

brainly.com/question/10439235

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