Question

Given f of x is equal to the quantity x plus 3 end quantity over the quantity x squared minus x minus 12 end quantity and g(x) = log4x, evaluate (g – f )(2).
negative one half
0
one half
1

Answer 1

From the given f(x) and g(x), the value of (g-f)(2)=1

Given :

The functions are

$f(x)=\frac{x+3}{x^2-x-12} \\g(x)=log_4(x)$

Lets evaluate (g-f)(2)

$(g-f)(2)=g(2)-f(2)$

To find out g(2), replace 2 for x  in g(x) and then replace 2 for x in f(x)

$f(x)=\frac{x+3}{x^2-x-12} \\g(x)=log_4(x)\\x=2\\f(2)=\frac{2+3}{2^2-2-12}=\frac{5}{-10}=-\frac{1}{2} \\\\g(2)=log_4(2)=\frac{1}{2}$

Now we find g(2)-f(2)

$(g-f)(2)=g(2)-f(2)=\frac{1}{2}-\frac{-1}{2} =1$

Learn more :  brainly.com/question/15038769