How do you confirm that f and g are inverses by showing that f(g(x))=x and g(f(x))=x ?
Problem: f(x)=3x-2 and g(x)= x+2
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3
Please help, don't know where to begin?
I will do the first
f(g(x))=f(x+2)=(3(x+2)-2)=6x+4 Hmmmm.
g(f(x))=g(3x-2)=3x-2+2=3x
What makes you think they are inverses?
I didn't see the denominator because of the margin. So do it the way I did, (Put the denominator in), and if they are inverses, both will equal x.
To confirm that f and g are inverses, we need to show that f(g(x)) = x and g(f(x)) = x for any x value.
Let's begin with f(g(x)):
1. Replace g(x) in f(g(x)) with its expression: f(g(x)) = f(x + 2).
2. Replace f(x) in f(x + 2) with its expression: f(g(x)) = 3(x + 2) - 2.
3. Simplify the expression: f(g(x)) = 3x + 6 - 2 = 3x + 4.
Now, let's move on to g(f(x)):
1. Replace f(x) in g(f(x)) with its expression: g(f(x)) = g(3x - 2).
2. Replace g(x) in g(3x - 2) with its expression: g(f(x)) = (3x - 2) + 2.
3. Simplify the expression: g(f(x)) = 3x.
Now, we can conclude:
f(g(x)) = 3x + 4
g(f(x)) = 3x
Since f(g(x)) = x and g(f(x)) = x for any x value, we can confirm that f and g are inverses.