Question

suppose that the functions s and t are defined for all real numbers x as follows. s(x)=2x+6 t(x)=3x. write the expressions for (s+t)(x) and (s*t)(x) and evaluate (s-t)(4)

Answer 1

s(x)=2x+6

t(x)=3x

For (s+t)(x) add both functions:

(s+t)(x) = 2x+6+3x

Combine like terms

(s+t)(x)= 2x+3x+6

(s+t)(x)= 5x+6

(s*t)(x) , muitiply both:

(s*t)(x) = (2x+6) (3x)

Apply distributive property:

(s*t)(x) =2x(3x)+6(3x)

(s*t)(x) = 6x^2+18x

(s-t)(4)​; subtract and replace x by 4

(s-t)(4)​ = 2(4)+6 -3(4)

(s-t)(4)​= 8+6-12

(s-t)(4)​= 2