If f and g are inverse functions, f (7) =10 and f (10) = −1 , find g(10).
To find g(10), we need to use the fact that f and g are inverse functions.
Since f(7) = 10, this tells us that g(10) = 7. This is because if f and g are inverse functions, then applying g after f should give us back the original value, and applying f after g should also give us back the original value.
So, in this case, f(g(10)) = 10. But we know that f(7) = 10, so this means g(10) = 7.
Therefore, g(10) = 7.
Inverse function has one peculiar property:
if g is the inverse function of f, and the domain of both is (-∞,∞), then
f(g(x))=x
and inversely
g(f(x))=x
From information above, what would g(f(7)) give?