Question

The function f is defined by f(x) = x^2 + 3x -10 , if f(x + 5) = x^2 + kx + 30, k=

Answer 1

k = 13

Explanation:

substitute x = x + 5 into f(x) , that is

f(x + 5) = (x + 5)² + 3(x + 5) - 10 ← expand squared factor using FOIL

= x² + 10x + 25 + 3x + 15 - 10

= x² + 13x + 30

compare this with f(x + 5) = x² + kx + 30

for the 2 expressions to be equal , then k = 13