If f(x)=10x - 10, what is the value of (f °f^-1)(-10)?

Question

isaidavila · Answer

(F°F^-1)=10(1/10x-10)-10
I think culd be that

michele_laino · Answer

hint:
we have this:
$$\Large   f\left( 0 \right) =  - 10 \Rightarrow {f^{ - 1}}\left( { - 10} \right) = 0$$

anonymous · Answer

So f^-1 is 10? Sorry, I don't really get this

michele_laino · Answer

by definition, we have:
$$\Large  \left( {f \circ {f^{ - 1}}} \right)\left( { - 10} \right) = f\left\{ {{f^{ - 1}}\left( { - 10} \right)} \right\} = ...$$

michele_laino · Answer

another step:
$$\Large  \left( {f \circ {f^{ - 1}}} \right)\left( { - 10} \right) = f\left\{ {{f^{ - 1}}\left( { - 10} \right)} \right\} = f\left( 0 \right) = ...?$$

anonymous · Answer

Is it 0? Because anything times 0 is 0?

dumbcow · Answer

a function and its inverse cancel themselves out
$$f(f^{-1} (x)) = x$$
$$f^{-1}(f(x)) = x$$

anonymous · Answer

I'll keep that in mind. Thanks 🐢 I just put 0, since it wasn't for a grade anyways lol The answer was apparently -10. Could you please explain why?