Question

Suppose that the functions s and t are defined for all real numbers x as follows. s(x) = x+4 t(x) = 2x^2 Write the expressions for (s+t) (x) and (s*t) (x) and evaluate (s-t)(3).

Answer 1

The expression (s+t)(x) is the same as s(x) + t(x), and the expression (s*t)(x) is the same as s(x) * t(x).

So, calculating these expressions, we have:

`\begin{gathered} (s+t)(x)=s(x)+t(x) \\ =x+4+2x^2 \\ 2x^2+x+4 \\ \\ (s\cdot t)(x)=s(x)\cdot t(x) \\ =(x+4)\cdot(2x^2) \\ =2x^3+8x^2 \end{gathered}`

Now, evaluating the expression (s-t)(3), we have:

`\begin{gathered} (s-t)(x)=s(x)-t(x) \\ =x+4-2x^2 \\ \\ (s-t)(3)=(3)+4-2\cdot(3)^2_{} \\ =7-2\cdot9 \\ =7-18 \\ =-11 \end{gathered}`

So the value of the expression (s-t)(3) is -11.