Answer:
The answer is B.
Step-by-step explanation:
Since f(x) = 4x + 1 and g(x) = x^2 - 5, 4x + 1 can be substituted for f and x^2 - 5 can be substituted for g in the equation (g/f)(x). Keep in mind that the x after (g/f) is just saying that (g/f) is a function of x, which means that it changes depending on the value of x. The x is not involved in any of the calculations, only the g and f values are. Knowing that x^2 - 5 substitutes for g and 4x + 1 substitutes for f, the equation would be (x^2 - 5/4x + 1) which means that answers A and C can be eliminated. After that, the only remaining answers are B and D, and the only difference between them is that B says that x cannot be equal to -1/4. This is true because the denominator of a fraction cannot be equal to 0 and plugging in -1/4 for x would give 4(-1/4) + 1 which would be equal to -1 + 1 which is equal to 0. The reason why a denominator of a fraction cannot be equal to 0 is because it is impossible to divide by 0 (unless the numerator is also 0) as dividing by 0 will not grant an answer because no matter how many times it is multiplied it will not ever equal the number that it was trying to go into.
