Question

Suppose that the functions s and t are defined for all real numbers x as follows.

Answer 1

Answer:

$(s + t)(x)= 5x+1$

$(s - t)(x)= -3x-5$

$(s.t)(1) = -7$

Step-by-step explanation:

Given

$s(x) = x - 2$

$t(x) = 4x + 3$

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

This is calculated as:

$(s + t)(x)= s(x) + t(x)$

$(s + t)(x)= x-2 + 4x + 3$

Collect like terms

$(s + t)(x)= x+ 4x-2 + 3$

$(s + t)(x)= 5x+1$

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

This is calculated as:

$(s - t)(x)= s(x) - t(x)$

$(s - t)(x)= x-2 - 4x - 3$

Collect like terms

$(s - t)(x)= x- 4x-2 - 3$

$(s - t)(x)= -3x-5$

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

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

This is calculated as:

$(s.t)(x) = s(x)* t(x)$

So, we have:

$(s.t)(x) = (x - 2) * (4x + 3)$

Substitute 1 for x

$(s.t)(1) = (1 - 2) * (4*1 + 3)$

$(s.t)(1) = - 1 * 7$

$(s.t)(1) = -7$