Question

suppose that the functions s and t are defined for all real numbers x as follows. s(x)=4x-5 t(x)=x+6 write the expression for (s+t)(x) and (s•t)(x) and evaluate (s-t)(2)

Answer 1

To find the expression for (s+t)(x), we simply add the two functions s(x) and t(x): (s + t)(x) = s(x) + t(x) = 4x - 5 + x + 6 = 5x + 1

To find the expression for (s•t)(x), we multiply the two functions s(x) and t(x): (s•t)(x) = s(x) * t(x) = (4x - 5) * (x + 6) = 4x^2 + 19x - 30

To evaluate (s-t)(2), we substitute 2 for x in the expression for (s-t)(x): (s-t)(2) = s(2) - t(2) = (4*2 - 5) - (2 + 6) = 3 - 8 = -5

Therefore, the expression for (s+t)(x) is 5x+1, the expression for (s•t)(x) is 4x^2+19x-30, and (s-t)(2) is -5.

Explanation: