Question

Find f(a), f(a + h), and the difference quotient (f(a + h) - f(a))/h, where h ≠ 0. f(x) = x/x²

a) 1/a, 1/(a + h), h/(a(a + h))
b) a/1, (a + h)/(a + h)², h/(a(a + h))
c) 1/a, 1/(a + h), h/(a + h)²
d) a/1, (a + h)/(a(a + h)), h/(a + h)²

Answer 1

For the function f(x) = x/x², f(a) is 1/a, f(a + h) is 1/(a + h), and the difference quotient is -h/(a(a + h)).

Step-by-step explanation:

The question is asking us to find the values for f(a), f(a + h), and the difference quotient (f(a + h) - f(a))/h for the function f(x) = x/x² where h ≠ 0. To find f(a), we substitute 'a' into the function, which results in f(a) = a/a² = 1/a. Similarly, to find f(a + h), we substitute 'a + h' into the function to get f(a + h) = (a + h)/(a + h)² = 1/(a + h). Lastly, to determine the difference quotient, we subtract f(a) from f(a + h) and then divide by h, which yields:

((a + h)/(a + h)² - a/a²)/h

=(1/(a + h) - 1/a)/h

=((a - (a + h))/(a(a + h)))/h

=(-h/(a(a + h)))/h

= -1/(a(a + h))