Question

g(x)=-x^2+2x, Find g(1/g(a))

Answer 1

please compute g(a) first

Answer 2

in order to that, it is suffice to set x=a into the formula for g(x)

Answer 3

okay so then you get g(a)=a^2+2a @Michele_Laino

Answer 4

please, be careful with sign, since you have:
\[g(a)=-a ^{2}+2a\]

Answer 5

Now, please you have to set
\[x=\frac{ 1 }{ -2a ^{2}+2a }\]
into your formula for g(x)

Answer 6

oops..
\[x=\frac{ 1 }{ -a ^{2}+2a }\]

Answer 7

what do you get?

Answer 8

wouldnt that be the answer? I cant see anything I have to simplify

Answer 9

note that you have to compute this quantity:
\[-\left( \frac{ 1 }{ -a ^{2}+2a } \right)^{2}+2\left( \frac{ 1 }{ -a ^{2}+2a } \right)\]

Answer 10

hint:
\[-\left( \frac{ 1 }{ -a ^{2}+2a } \right)^{2}+\frac{ 2 }{ -a ^{2}+2a }=\]

Answer 11

=\[-\frac{ 1 }{ (-a ^{2}+2a )^{2}}+\frac{ 2 }{ (-a ^{2}+2a) }=\]

Answer 12

\[=\frac{ -1+2(-a ^{2}+2a) }{ (-a ^{2}+2a)^{2} }=...\]
please continue