We are asked to compare the function f(x) to g(x). Let's find the simplified form of f(x) to see if it is similar to g(x).
f(x)=(3x−7)(3x−7)(x+6)=(3x−7)(3x−7)(x+6)=x+6
After canceling out common factors in the numerator and denominator of f(x), we see its simplified form is equal to g(x). Let's compare the domains of the functions by taking a look at g(x) first.
g(x)=x+6
We see that there are no domain values that would make this function a forbidden calculation. Therefore, the domain for g(x) is all real numbers. Let's look at f(x).
f(x)=(3x−7)(3x−7)(x+6)
If the denominator of a fraction equals 0 then the expression becomes undefined. We must exclude all values from our domain that make our expression undefined. Let's set the denominator of f(x) equal to 0 in order to solve for this value.
The value x=37 will make our function undefined. We can use this fact to write the domain of f(x).
Domain: x=37
We see that the expressions f(x) and g(x) have the same simplified form, but the domain of g(x) is all real numbers. The domain of f(x) is all real numbers except x=37.
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