Question

Suppose that the functions q and r are defined as follows.9(x)=-x+2r(x) = 4x+3Find the following.(9.r) (-4) =0口0/0(r• q) (-4) = 0X 5?

Answer 1

When two functions are composed it means that we insert one into the other.

For the first one

`q\cdot r=q(r(x))`

for that reason we insert the functio in the function q before finding the corresponding image for (-4)

`\begin{gathered} q(r(x))=-x+2 \\ q(r(x))=-(4x+3)+2 \\ q(r(x))=-4x-3+2 \\ q(r(x))=-4x-1 \end{gathered}`

then we find the value for x=-4

`\begin{gathered} (q\cdot r)(-4)=-4(-4)-1 \\ (q\cdot r)(-4)=16-1 \\ (q\cdot r)(-4)=15 \end{gathered}`

for the second one we od the opposite and insert function q into the function r

`r\cdot q=r(q(x))`
`\begin{gathered} r(q(x))=4x+3 \\ r(q(x))=4(-x+2)+3 \\ r(q(x))=-4x+8+3 \\ r(q(x))=-4x+11 \end{gathered}`

then we find the value for x=-4

`\begin{gathered} r(q(x))=-4x+11 \\ (r\cdot q)(-4)=-4(-4)+11 \\ (r\cdot q)(-4)=16+11 \\ (r\cdot q)(-4)=27 \end{gathered}`