The equation g(x) =x^2+4x-7 is a transformation of the function f(x) such that g(x) = f(x+5). Find the orignial function f(x)
f(x) = g(x-5) = (x-5)^2 + 4(x-5) - 7
you can expand that out if you want.
how do i do this question?
x = (x-5)+5
so, if g(x) = f(x+5),
g(x-5) = f(x-5 + 5) = f(x)
To find the original function f(x), we need to reverse the transformation applied to g(x). In this case, we are given that g(x) = f(x + 5). To find f(x), we need to calculate f(x) from g(x) by undoing the transformation.
Let's substitute (x + 5) back into the equation for g(x):
g(x) = f(x + 5)
x^2 + 4x - 7 = f(x + 5)
To undo the transformation, we substitute (x + 5) back into the equation and solve for f(x):
(x + 5)^2 + 4(x + 5) - 7 = f(x)
Expanding and simplifying:
x^2 + 10x + 25 + 4x + 20 - 7 = f(x)
x^2 + 14x + 38 = f(x)
Therefore, the original function f(x) is f(x) = x^2 + 14x + 38.