Question

Compute the following for the function defined below. Simplify your answers. Note: Use lowercase f(x)=2

−9x+7 (a) f(a)= (b) f(a+h)= (c) f(a+h)−f(a)= (d)
h
f(a+h)−f(a)
​
= ig for the function defined below. Simplify your answers.

Answer 1

To compute the values of the function, we substitute and simplify: f(a) = 9 - 9a, f(a+h) = 9 - 9a - 9h, f(a+h) - f(a) = -9h, and h[f(a+h) - f(a)] = -9h².

Step-by-step explanation:

Computing Values of a Function

To compute the values of the function f(x) = 2 - 9x + 7 for different cases, follow these steps:

1. f(a) - Simply replace x with a in the function:
   f(a) = 2 - 9a + 7 = 9 - 9a.
2. f(a+h) - Replace x with a+h:
   f(a+h) = 2 - 9(a+h) + 7 = 9 - 9a - 9h.
3. f(a+h) - f(a) - Subtract f(a) from f(a+h):
   (9 - 9a - 9h) - (9 - 9a) = -9h.
4. h[f(a+h) - f(a)] - Multiply the difference by h:
   h(-9h) = -9h².

This simplifies each expression to its most basic form.