The graph of f(x) passes through the point (-6, 4). Find the corresponding point on the graph of g^-1 if g(x)=3f(3x)-4
g(-2) = 3f(-6)-4 = 8
g^-1(8) = -2
Allright, got it! Thank you for your help =)
To find the corresponding point on the graph of g^-1, we first need to find the value of g^-1(-6) given that g(x) = 3f(3x) - 4.
To find g^-1(-6), we start by substituting -6 into the equation for g(x):
g(-6) = 3f(3(-6)) - 4
Next, we find the value of f(3(-6)) using the given point (-6, 4) on the graph of f(x). Since the graph of f(x) passes through the point (-6, 4), we can substitute x = -6 into f(x) to find the corresponding y-value:
f(-6) = 4
Now we substitute this value into the equation for g(x):
g(-6) = 3f(3(-6)) - 4
= 3f(-18) - 4
Since f(-6) = 4, we can substitute it in and simplify:
g(-6) = 3(4) - 4
= 12 - 4
= 8
So, we have found that g(-6) = 8.
Now, to find the corresponding point on the graph of g^-1, we set g^-1(-6) = 8 and solve for x:
g^-1(8) = -6
Therefore, the corresponding point on the graph of g^-1 is (-6, 8).