Explanation:
A. To find f(x+h), we substitute (x+h) for x in the equation f(x) = 4x + 7:
f(x+h) = 4(x+h) + 7
Expanding the brackets:
f(x+h) = 4x + 4h + 7
Simplifying, we get:
f(x+h) = 4x + 7 + 4h
Therefore, f(x+h) = 4x + 7 + 4h.
B. To find f(x+h)-f(x)/h, we use the formula for the difference quotient:
[f(x+h) - f(x)] / h
Substituting the expressions we derived earlier:
[f(x+h) - f(x)] / h = [(4x + 7 + 4h) - (4x + 7)] / h
Simplifying, we get:
[f(x+h) - f(x)] / h = (4x + 4h - 4x) / h
Canceling out the 4x terms, we get:
[f(x+h) - f(x)] / h = 4h / h
Simplifying further, we get:
[f(x+h) - f(x)] / h = 4
Therefore, f(x+h)-f(x)/h = 4.