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Suppose that the functions s and t are defined for all real numbers x as follows.
s (x)=x-2
t(x) = 4x+3
Write the expressions for (s +t)(x) and (s – t)(x) and evaluate (s.t)(1).

Respuesta :

MrRoyal

Answer:

[tex](s + t)(x)= 5x+1[/tex]

[tex](s - t)(x)= -3x-5[/tex]

[tex](s.t)(1) = -7[/tex]

Step-by-step explanation:

Given

[tex]s(x) = x - 2[/tex]

[tex]t(x) = 4x + 3[/tex]

Solving (a): (s + t)(x)

This is calculated as:

[tex](s + t)(x)= s(x) + t(x)[/tex]

[tex](s + t)(x)= x-2 + 4x + 3[/tex]

Collect like terms

[tex](s + t)(x)= x+ 4x-2 + 3[/tex]

[tex](s + t)(x)= 5x+1[/tex]

Solving (b): (s - t)(x)

This is calculated as:

[tex](s - t)(x)= s(x) - t(x)[/tex]

[tex](s - t)(x)= x-2 - 4x - 3[/tex]

Collect like terms

[tex](s - t)(x)= x- 4x-2 - 3[/tex]

[tex](s - t)(x)= -3x-5[/tex]

Solving (b): (s . t)(1)

First, we calculate (s.t)(x)

This is calculated as:

[tex](s.t)(x) = s(x)* t(x)[/tex]

So, we have:

[tex](s.t)(x) = (x - 2) * (4x + 3)[/tex]

Substitute 1 for x

[tex](s.t)(1) = (1 - 2) * (4*1 + 3)[/tex]

[tex](s.t)(1) = - 1 * 7[/tex]

[tex](s.t)(1) = -7[/tex]

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