Suppose that the dunctions q and r are defined as follows. q(x)=x^2+5 r(x)=sqrt(x+3) Find the following. q@r(1)=? (r@q)(1)=?

Question

Suppose that the dunctions q and r are defined as follows.

q (x) = x^{2} + 5

r (x) = \sqrt{x + 3}

Find the following.

q \circ r (1) = ?

(r \circ q) (1) = ?

Answer 1

The composition of the function f(x) and g(x) is denoted by $f \circ g (x)$ is:
$(q \circ r) (1) = q (r (1))$
$= q (\sqrt{1 + 3}) {:^{'} r (x) = \sqrt{x + 5}}$
$= q (2)$
$= 2^{2} + 5^{'} q (x) = x^{2} + 5}$
=4+5
=9
Compute the value of composite function $(r \circ q) (1) :$
$(r \circ q) (1) = r (q (1))$
$= r (1^{2} + 5) {:^{'} q (x) = x^{2} + 5}$
$= r (6)$
$= \sqrt{6 + 5} {:^{'} r (x) = \sqrt{x + 5}}$
$= \sqrt{11}$

Suppose that the dunctions q and r are defined as follows. q(x)=x^2+5 r(x)=sqrt(x+3) Find the following. q@r(1)=? (r@q)(1)=?

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