Final answer:
The function f(x+h) is found by substituting x with x+h in the expression 7x - 9, resulting in 7x + 7h - 9. Simplifying f(x+h) - f(x) over h, the h terms cancel out, leaving the simplified result of 7.
Step-by-step explanation:
To answer part (a) of the given mathematical problem, we need to find f(x+h). The function f(x) is defined as f(x) = 7x - 9. Thus, to find f(x+h), we replace x with (x+h) in the original function. This gives us:
f(x+h) = 7(x+h) - 9
Now, we simplify the expression by distributing the 7:
f(x+h) = 7x + 7h - 9
Next, to address part (b) of the question, we need to find f(x+h) - f(x) and then divide that by h. Substituting the expressions for f(x+h) and f(x), we get:
f(x+h) - f(x) = (7x + 7h - 9) - (7x - 9)
We eliminate terms wherever possible to simplify the algebra. Cancelling out the like terms, we are left with:
f(x+h) - f(x) = 7h
Then, when we divide by h, the h's cancel out, leaving us with the result:
(f(x+h) - f(x)) / h = 7
After simplifying, we check the answer to see if it is reasonable. In this case, the simplification process appears correct and the answer is indeed reasonable.