Find each function, find f(a+h) and f(a+h)-f(a)
a) f(x)=5x-2
5(a+h) -2 = 5a + 5h - 2
5(a) -2 = 5 a - 2
--------------------------subtract
5 h is the answer
now if we were doing calculus we would divide that by h and then let h go to 0
5 h/h = 5
and we call that the "derivative" of f(x)=5x-2
May I know where you got 5a + 5h - 2
f(a+h) = 5(a+h) - 2
from your function definition
5(a+h) -2 = 5 a + 5 h - 2
Thank you~
To find f(a+h), you need to substitute the expression a+h into the function f(x).
For function a):
f(x) = 5x - 2
To find f(a+h), replace every x in the function with (a+h):
f(a+h) = 5(a+h) - 2
Now, simplify the expression:
f(a+h) = 5a + 5h - 2
To find f(a+h) - f(a), subtract f(a) from f(a+h):
f(a+h) - f(a) = (5a + 5h - 2) - (5a - 2)
Simplifying further:
f(a+h) - f(a) = 5a + 5h - 2 - 5a + 2
The terms with 5a and -5a cancel each other out:
f(a+h) - f(a) = 5h
Therefore, f(a+h) - f(a) = 5h for the given function.