Find f(a + h) − f(a) for the function. Simplify your answer. f(x) = − 1/ 2 x + 5

Answer 1

This question is a substitution question in which what is in parentheses will be exchanged or substituted. In other words, when you see f(x) and x in the equation, you'll want to substitute f(a+h) and a+h in the equation.

So, instead of writing f(x)=-1/2(x)+5 you'll want to write f(a+h)= - 1/2 (a+h) + 5. Solving this part would then give you -1/2a -1/2 h + 5.

Then you'll have to do the second part which is -f(a). You'll make everything in the equation negative and substitute all the x for a. So, you'll get -f(a)= +1/2a - 5.

The last step is simply adding together these two parts so f(a+h) - f(a) = -1/2a - 1/2h + 5 +1/2a - 5. The a values cancel out or add to zero since one is positive and one is negative and +5 and -5 also cancel out.

Thus, your answer is +1/2a.