Let f (x) = x + 3. Find and simplify :
f(a+h)−f(a) /h
just plug and chug
f(a+h)-f(a) = (a+h+3)-(a+3) = h
so,
f(a+h)-f(a)
------------ = h/h = 1
h
I'm sorry its supposed to be the square root of x+3, would it end up being the same ??
To find and simplify the expression (f(a+h) - f(a)) / h, we will start by substituting the given function f(x) = x + 3 into the expression.
Step 1: Substitute f(x) = x + 3 into the expression.
(f(a+h) - f(a)) / h = ((a+h) + 3 - (a + 3)) / h
Step 2: Simplify the expression inside the numerator.
((a+h) + 3 - (a + 3)) = (a + h + 3 - a - 3)
= (a - a) + (h - 3 + 3)
= 0 + h
= h
Step 3: Substitute the simplified numerator back into the expression.
((a+h) + 3 - (a + 3)) / h = h / h
Step 4: Simplify the expression.
h / h = 1
Therefore, the expression (f(a+h) - f(a)) / h simplifies to 1.