Question

Given f(x)= (x+3)/x²-4x-21 and g(x)=log _4x , evaluate (g-f)(8)

Answer 1

To evaluate (g-f)(8), substitute 8 into both g(x) and f(x), subtract f(8) from g(8), and simplify the result.

Step-by-step explanation:

To evaluate (g-f)(8), we need to substitute 8 into both g(x) and f(x) and then subtract the result of f(8) from g(8).

Using the given values of f(x) and g(x), we have:

g(8) = log4(8) = log423 = 3/2

f(8) = (8+3)/(8²-4(8)-21) = 11/9

Therefore, (g-f)(8) = g(8) - f(8) = 3/2 - 11/9 = (27-22)/18 = 5/18.