Question

Suppose that the functions s and I are defined for all real numbers x as follows.s(x) = x³t(x) = 5x²Write the expressions for (t•s) (x) and (t-s) (x) and evaluate (t+s) (-1).(t*•s)(x) = 0

Answer 1

Given that,

The functions s and t are defined for all real numbers x as follows,

`\begin{gathered} s\left(x\right)=x^3 \\ t\left(x\right)=5x^2 \end{gathered}`

To find the expressions for (t•s) (x) and (t-s) (x)

To evaluate (t+s) (-1).

Step-by-step explanation:

we have that,

`\left(t•s\right)x=t(x)•s(x)`

Substitute the values we get,

`\left(t•s\right)x=(5x^2)(x^3)`
`\left(t•s\right)x=5x^5`

To find (t-s) (x)

we get,

`\left(t-s\right)x=t(x)-s(x)`
`\left(t-s\right)x=5x^2-x^3`

To evaluate (t+s) (-1)

`\left(t+s\right)(x)=t(x)+s(x)`

we get,

`\left(t+s\right)(x)=5x^2+x^3`

Put x=-1, we get

`\left(t+s\right)(-1)=5(-1)^2+(-1)^3`
`(t+s)(-1)=5-1`
`(t+s)(-1)=4`

Answers are:

`\left(t•s\right)x=5x^5`

`\left(t-s\right)x=5x^2-x^3`

`(t+s)(-1)=4`