Question

Given f(x)=8x²−1, find and simplify the difference quotient f(x)−f(a)/x-a.

a) 16x+8a+1
b) 8x2−1
c) 8x+a
d) 16x−8a−1

Answer 1

To find the difference quotient for the given function, substitute x and a into the function and simplify the expression. The difference quotient simplifies to 8(x + a).

Step-by-step explanation:

To find the difference quotient for the function f(x) = 8x^2 - 1, we need to substitute x and a into the function and simplify the expression.

The difference quotient is given by (f(x) - f(a))/(x - a).

Substituting the function f(x) = 8x^2 - 1 into the difference quotient, we get:

((8x^2 - 1) - (8a^2 - 1))/(x - a)

Simplifying the expression, we have:

(8x^2 - 8a^2)/(x - a)

Factoring out the common factor of 8, we can rewrite the expression as:

8(x^2 - a^2)/(x - a)

Using the difference of squares formula, x^2 - a^2 can be factored as (x + a)(x - a). Therefore, the difference quotient simplifies to:

8(x + a)