linear functions if g(fx) = 2x+6
f(gx) is a line through origin
what is f(g2011)
To find the value of f(g2011), we need to know the function g(x).
The given information tells us that g(fx) = 2x + 6.
To compute f(g2011), we need to find the value of g2011 and substitute it into the function f(x).
Before we can find g2011, we need to know the function g(x). Let's assume g(x) is a linear function of the form g(x) = mx + b, where m is the slope of the line and b is the y-intercept.
Since f(gx) is a line passing through the origin, it means that f(0) = 0 (since f(0) will be the y-intercept of the line).
Substituting gx as 0, we have f(0) = 2(0) + 6 = 6.
So, f(0) = 6 and this implies that b = 6.
Now, let's substitute gx as 2011 in g(fx) = 2x + 6 and solve for fx:
2(f(2011)) + 6 = 2011
2(f(2011)) = 2011 - 6
2(f(2011)) = 2005
f(2011) = 2005/2
Therefore, f(g2011) = 2005/2.