Question

If g is a function defined over the set of all real numbers and g(x-1)=3x^(2)+5x-7, then which of the following defines g(x) ? (A) g(x)=3x^(2)-x-9 (B) g(x)=3x^(2)+5x+1 (C) g(x)=3x^(2)+11x+1 (D) ,g(x)=3x^(2)+11x-6

Answer 1

To find the function g(x), substitute x-1 into g(x-1) = 3x² + 5x - 7 and simplify the equation.

Step-by-step explanation:

To find the function g(x), we need to substitute x-1 into g(x-1) = 3x² + 5x - 7

g(x-1) = 3(x-1)² + 5(x-1) - 7

= 3(x² - 2x + 1) + 5(x - 1) - 7

= 3x² 6x + 3 + 5x - 5 - 7

= 3x² - x - 9

So, the correct option is (A) g(x) = 3x² - x - 9

Answer 2

To find g(x) when given g(x-1) = 3x^2 + 5x - 7, replace x in the equation with (x+1), simplify and the function g(x) is found to be 3x^2 + 11x + 1, which corresponds to option (C).

Step-by-step explanation:

If g is a function defined over the set of all real numbers and given g(x-1) = 3x^2 + 5x - 7, to find g(x), we can replace each occurrence of x in g(x-1) with (x+1). This makes g(x) = 3(x+1)^2 + 5(x+1) - 7. Expanding it:

g(x) = 3(x^2 + 2x + 1) + 5x + 5 - 7

g(x) = 3x^2 + 6x + 3 + 5x - 2

g(x) = 3x^2 + 11x + 1

Therefore, the correct answer is (C) g(x) = 3x^2 + 11x + 1.