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)=(2x^2-7x+3)/(x-3) f(x)=(2x+1)
g(x)=(2x^2-7x+3)/(x-3)
= (x-3)(2x-1)/(x-3)
= 2x-1 , x ≠ 3
≠ f(x)
To determine if the function f(x) is the simplified form of g(x), we need to compare the two functions and check if they are equivalent.
First, let's compare the simplified forms of g(x) and f(x):
g(x) = (2x^2 - 7x + 3)/(x - 3)
f(x) = 2x + 1
It's clear that the two functions are different as g(x) is a rational function, while f(x) is a linear function.
To find the simplified form of g(x), we can perform polynomial division or factorization. Let's perform polynomial division:
2x - 1
______________
x - 3 | 2x^2 - 7x + 3
- (2x^2 - 6x)
______________
-x + 3
- (-x + 3)
______________
0
From polynomial division, we find that g(x) = 2x - 1.
So, f(x) is not the simplified form of g(x). The corrected simplified form of g(x) is g(x) = 2x - 1.
Regarding the non-permissible values, we need to identify any values of x that would make the denominator of g(x) or f(x) equal to zero since division by zero is undefined.
For g(x), the denominator is (x - 3), so the non-permissible value is x = 3.
For f(x), there is no denominator, so there are no non-permissible values.
Therefore, the corrected simplified form of g(x) is g(x) = 2x - 1, and the non-permissible value is x = 3.