Question

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

Answer 1

In order to find the expression for (t*s)(x), let's multiply the functions t(x) and s(x):

`(t\cdot s)(x)=t(x)\cdot s(x)=4x^3\cdot x^2=4x^5`

To find the expression for (t-s)(x), let's subtract t(x) and s(x):

`(t-s)(x)=t(x)-s(x)=4x^3-x^2`

Now, to evaluate the expression (t+s)(2), let's find (t+s)(x) and then use x = 2:

`\begin{gathered} (t+s)(x)=t(x)+s(x)=4x^3+x^2\\ \\ (t+s)(2)=4(2)^3+(2)^2=4\cdot8+4=36 \end{gathered}`