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Olegator [25]
3 years ago
9

For f(x)= 3x+1 and g(x)= x^2-6, find (g/f)(x).

Mathematics
2 answers:
o-na [289]3 years ago
4 0
D. The exclusion is important because we cannot divide by zero. Apart from that we are simply looking at a function. 
Anton [14]3 years ago
3 0

Answer:

A. \frac{x^2+6}{3x+1}, x\neq -\frac{1}{3}

Step-by-step explanation:

Given functions,

f(x) = 3x + 1

g(x) = x^2 - 6

∵ (\frac{g}{f})(x) = \frac{g(x)}{f(x)}

By substituting the values,

(\frac{g}{f})(x)=\frac{x^2-6}{3x+1}

Which is a rational function,

We know that,

A rational function is defined for all real numbers except those for which denominator = 0,

If 3x+1 = 0

\implies 3x = -1

\implies x =-\frac{1}{3}

i.e. domain restriction of g/f is x≠ -1/3

Hence, OPTION D is correct.

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