Question

Let f(x)=−7x+1. Then the expression hf(x+h)−f(x) can be written in the form Ah+Bx+C, where A, B, and C are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants.

Answer 1

Answer:

A= 0,

B=0,

C=-7

Step-by-step explanation:

if f(x) = -7x +1 , then $\frac{ f(x+h)-f(x)}{h}$ can be written as Ah+Bx+C

f(x+h) = -7 (x+h) +1 = -7x - 7h +1

f(x+h) - f(x) =  -7x - 7h +1 - (-7x +1) =  -7x - 7h +1 +7x -1

f(x+h) - f(x) = - 7h

$\frac{ f(x+h)-f(x)}{h}$ = -7 =Ah+Bx+C

Ah+Bx+C = 0h+0x-7 = -7

Here:

A= 0,

B=0,

C=-7