Question

suppose that the functions s and t defined for all real numbers X as followsS(x)=4x-2T(x)=5xWrite the expression for the following

Answer 1

The operation (s-t)(x) subtracts the two functions given. We have

$\begin{gathered} (s-t)(x)=4x-2-5x \\ (s-t)(x)=-x-2 \end{gathered}$

The operation (s+t)(x) adds up the two functions given. We have

$\begin{gathered} (s+t)(x)=4x-2+5x \\ (s+t)(x)=9x-2 \end{gathered}$

The operation (s*t)(x) multiplies the two functions given. We have

$\begin{gathered} (s\cdot t)(x)=(4x-2)(5x)_{}_{} \\ (s\cdot t)(x)=20x^2-10x \end{gathered}$

The resulting function will be evaluated at x = 2. We have

$\begin{gathered} (s\cdot t)(2)=20(2)^2-10(2) \\ (s\cdot t)(2)=80-20 \\ (s\cdot t)(2)=60 \end{gathered}$

Hence, the answers to these problems are

1. (s-t)(x)=-x-2

2. (s+t)(x)=9x-2

3. (s*t)(2)=60