Question

PLEASE HELP!!! Given the functions, f(x) = 6x + 2 and g(x) = x - 7, perform the indicated operation. When applicable, state the domain restriction. (f/g)(x)

Answer 1

Answer:

The domain restriction for (f/g)(x) is x=7

Step-by-step explanation:

we have

$f(x)=6x+2$

$g(x)=x-7$

so

$(f/g)(x)=\frac{6x+2}{x-7}$

Remember that

the denominator can not be equal to zero

so

Find the domain restriction

x-7=0

x=7

therefore

The domain is all real numbers except the number 7

(-∞,7)∪(7,∞)

Answer 2

Answer with Step-by-step explanation:

We are given that:

$f(x)=6x+2$

and $g(x)=x-7$

So,

$(f/g)(x)=\dfrac{f(x)}{g(x)}$

$(f/g)(x)=\dfrac{6x+2}{x-7}$

For the above function to be well defined  the denominator has to be non-zero

So,

the domain restriction  is:

x-7≠0

x≠7

Therefore

The domain is all real numbers except the number 7

i.e. the domain is: (-∞,7)∪(7,∞)