Final answer:
To calculate f(x + h) - f(x) for the expression f(x) = 7x - 1, substitute x + h for x and subtract f(x) from it. The simplified expression is 7h.
Step-by-step explanation:
To calculate f(x + h) - f(x) for the expression f(x) = 7x - 1, we substitute x + h for x in the expression and then subtract f(x) from it:
f(x + h) - f(x) = 7(x + h) - 1 - (7x - 1)
We simplify by distributing the 7 to both x and h:
f(x + h) - f(x) = 7x + 7h - 1 - 7x + 1
Cancelling out the 7x terms and the 1 terms, we are left with:
f(x + h) - f(x) = 7h