If f and g are inverse functions and the point (-3, 5) is on the graph of f, then the point ____ is on the graph of g
f(5) = -3
so,
g(-3) = 5
Since they are inverses, f(g(x)) = g(f(x)) = x
f(g(-3)) = f(5) = -3
g(f(5)) = g(-3) = 5
For something more familiar,
f = x^2
g = sqrt(x)
f(g(x)) = [sqrt(x)]^2 = x
g(f(x)) = sqrt(x^2) = x
f(3) = 9
g(9) = 3
Well, rats. I got it backwards
f(-3) = 5
g(5) = -3
The point (-3, 5) is on the graph of f, so on the graph of g, you can expect to find the point (5, -3). Just like how f flips the x and y coordinates, g flips them back! It's like a magical coordinate dance. Ta-da!
If f and g are inverse functions, it means that for any input x, the output of f is equal to the input of g, and vice versa.
Given that the point (-3, 5) is on the graph of f, it means that when x = -3, f(x) = 5.
Since f and g are inverse functions, if (-3, 5) is on the graph of f, then (5, -3) must be on the graph of g.
Therefore, the point (5, -3) is on the graph of g.
To find the point on the graph of the inverse function g, we can use the fact that f and g are inverse functions.
If (-3, 5) is on the graph of f, it means that when we input -3 into f, we get an output of 5. In other words, f(-3) = 5.
Since f and g are inverse functions, their inputs and outputs "reverse" each other. This means that if we input the output of f into g, we should get the original input value. So, g(5) should equal -3.
Therefore, the point (-3, 5) on the graph of f corresponds to the point (5, -3) on the graph of g.