consider the functions f(x)=9/x; and g(x)=9/x
what is f(g(x))?
give any values that need to be excluded
what is g(f(x))
give any values that need to be excluded?
are functions f and g inverse of each other?
To find f(g(x)), we substitute g(x) into f(x).
Given that g(x) = 9/x, we substitute it into f(x) as follows:
f(g(x)) = f(9/x) = 9 / (9/x)
To simplify this expression, we multiply the numerator (9) by the reciprocal of the denominator (1/x):
f(g(x)) = 9 * (x/9) = x
Therefore, f(g(x)) simplifies to x.
Now, to find g(f(x)), we substitute f(x) into g(x).
Given that f(x) = 9/x, we substitute it into g(x) as follows:
g(f(x)) = g(9/x) = 9 / (9/x)
Just like before, we simplify this expression by multiplying the numerator (9) by the reciprocal of the denominator (1/x):
g(f(x)) = 9 * (x/9) = x
Therefore, g(f(x)) simplifies to x as well.
Since we have f(g(x)) = x and g(f(x)) = x, this indicates that f(x) and g(x) are inverses of each other.