Question

Assume g is a one-to-one function. If g(x)=x^2+10x with x>-5, find g^-1(10)

Answer 1

you need to solve:
\[10 = x^2+10x\]
This is going to return 2 answers, and you pick the one that is greater than -5

Answer 2

but it is g^-1

Answer 3

thats right:
\[g^{-1}(10) \]
is the same as asking what value of x makes:
\[g(x) = 10\]
So we set g(x) = 10, and solve for x.

Answer 4

i thought you have to do something special... i thought like this:
lets call g^-1(x) = a
g^-1(x)= a^2 +10a
so it would turn out the same in this problem but in others it might be different right? i kinda forget even though i learned this like this year haha

Answer 5

hmm...thats sorta right. if you see it like that, it would be:
\[g^{-1}(10) = a\]
\[g(x) = x^2+10x \Rightarrow 10 = a^2+10a\]
and you would have to solve for a.

Answer 6

yeah ok thanks for the clarification!