Question

suppose that the functions r and s are defined for all real numbers x as follows. r(x)=x+5 s(x)=3x^2. write the expressions for (r-s)(x) and (r+s)(x) and evaluate (r*s)(-2)

Answer 1

The initial functions are:

$\begin{gathered} r(x)=x+5 \\ s(x)=3x^2 \end{gathered}$

Now we can add the functions so:

$(r+s)(x)=3x^2+x+5$

and we can rest the functions so:

$(r-s)(x)=x+5-3x^2$

and finally we can multiply the functions so:

$\begin{gathered} (r\cdot s)(x)=(x+5)(3x^2) \\ (r\cdot s)(x)=3x^3+15x^2 \end{gathered}$

and we can evaluate this new function in -2 so:

$\begin{gathered} (r\cdot s)(-2)=3(-2)^3+15(-2)^2 \\ (r\cdot s)(-2)=3\cdot(-8)+15\cdot(4) \\ (r\cdot s)(-2)=-24+60 \\ (r\cdot s)(-2)=36 \end{gathered}$