Answer:
[tex] \frac{x^2 - 5}{4x + 1} [/tex], x ≠ -1/4
Explanation:
We are given that:
f (x) = 4x + 1
g(x) = x² - 5
We want to find the value of (g/f)(x). This means that we will simply divide g(x) by f(x) as follows:
[tex]( \frac{g}{f} )(x) = \frac{g(x)}{f(x)} = \frac{x^2 - 5}{4x + 1} [/tex]
Now, we should note that any function is undefined if its denominator is equal to zero.
This means that for our current function:
4x + 1 cannot be equal to zero
4x + 1 = 0
4x = -1
x = -1/4
This means that the value of x cannot be -1/4, otherwise, our function would be undefined.
Based on the above, the last option is the correct one.
Hope this helps :)
