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Question

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

 

s (x) = x -3

t (x)=3x +5

 

write the expressions for (s• t) (x) and (s+t) (x) and evaluate (s-t)(-2)

Answer 1

Hi Kyle,

 

(s o t)(x) is the composite function of s(x) and t(x) and can be expressed as

(s o t)(x) = s(t(x)) This means that we will plug in t(x) for x in s(x).

(s o t)(x) = (3x + 5) - 3

= 3x + 2

 

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

= (x - 3) + (3x + 5)

= 4x + 2

 

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

=  (x - 3) - (3x + 5)

= x - 3 - 3x - 5

= -2x - 8

Then,

(s - t)(-2) = -2*(-2) - 8

= 4 - 8

= -4