Question

Q(x)=x^2 +3r(x)=square root of x+2find the following (q×r)(2)(r×q)(2)

Answer 1

Step 1 :

Suppose that the functions q and r are defined as follows:

`\begin{gathered} q(x)=x^2\text{ + 3} \\ r\text{ ( x ) = }\sqrt[]{x\text{ + 2}} \end{gathered}`

Step 2:

We need to find the value of:

`\begin{gathered} (q.r)(2)=(x^2\text{ + 3 ) }\sqrt[]{x\text{ + 2 }} \\ (q.r)(2)=(2^2\text{ + 3 ) }\sqrt[]{2\text{ + 2}} \\ =\text{ ( 4 + 3 ) }\sqrt[]{4} \\ =\text{ 7 x 2} \\ =\text{ 14} \end{gathered}`

Step 3 :

We also need to find the value of :

`\begin{gathered} (\text{ r . q ) ( 2 ) = }\sqrt[]{(\text{ x + 2)}}(x^2\text{ + 3)} \\ =\text{ ( }\sqrt[]{2\text{ + 2}})(2^2\text{ + 3 )} \\ =\text{ }\sqrt[]{4\text{ }}\text{ x ( 4 + 3)} \\ =\text{ 2 x 7} \\ =\text{ 14} \end{gathered}`