Determine if the function f(x) is the simplified form of g(x). If it is, state the non-permissible values. If it is not, determine the corrected simplified form, including the non-permissible values. (2 marks - show your work)
g(x)=6x^2+x-12/2x+3,f(x)=3x-4
To determine if the function f(x) is the simplified form of g(x), we need to simplify both functions and compare them.
1. Simplifying g(x):
g(x) = (6x^2 + x - 12) / (2x + 3)
To simplify, we can factor the numerator and denominator if possible.
g(x) = [(2x - 3)(3x + 4)] / (2x + 3)
Now we can see that the simplified form of g(x) is:
g(x) = (2x - 3)(3x + 4) / (2x + 3)
2. Simplifying f(x):
f(x) = 3x - 4
Function f(x) is already in simplified form.
3. Comparing g(x) and f(x):
f(x) = 3x - 4
g(x) = (2x - 3)(3x + 4) / (2x + 3)
By comparing the two functions, we can see that f(x) is not the simplified form of g(x) because their expressions are different.
Therefore, the corrected simplified form of g(x) is:
g(x) = (2x - 3)(3x + 4) / (2x + 3)
Non-permissible values for g(x) would be the values of x that make the denominator equal to zero since division by zero is undefined. In this case, the non-permissible value is x = -1.5 since it would make the denominator (2x + 3) equal to zero.