Question

Let

f(x)=x+36. Simplify or evaluate the expression
(f(6+h)–f(6))/h.

a) 1+ℎ
b)36
c) 1
d) 42+h

Answer 1

To solve the expression (f(6+h)–f(6))/h with f(x)=x+36, we evaluate f(6+h) and f(6), subtract them, and divide by h. Simplifying the expression, we get the result 1.

Step-by-step explanation:

The student is asking to simplify the expression (f(6+h)–f(6))/h where f(x) = x + 36. To solve this, we first find the value of f(6+h) by substituting x with 6+h in the function, which gives us (6+h) + 36. Then we find f(6), which is 6 + 36. We then subtract f(6) from f(6+h) and divide the result by h.

f(6+h) = (6+h) + 36
f(6) = 6 + 36

Plugging these into the expression, we get:

((6+h) + 36 - (6 + 36)) / h = (h + 42 - 42) / h = h/h = 1

Therefore, the simplified expression is 1.