Question

Functions.....
question below....

Answer 1

\[g(x)=8x-x^2\]
Find an expression, in terms of x, for \[g ^{-1}x\]

Answer 2

Write the function using y instead of f(x).
Then switch x and y.
Then solve for y. Then call y g^-1(x)

Answer 3

\[x=8y-y^2\]
is that it please??

Answer 4

@mathstudent55

Answer 5

@amistre64

Answer 6

that is correct enough yes; but in general, even powers have to have a modified inverse

Answer 7

\[g(x)=8x-x^2\]
\[-g(x)=x^2-8x\]
\[16-g(x)=x^2-8x+16\]
\[16-g(x)=(x-4)^2\]
\[\pm\sqrt{16-g(x)}=x-4\]
\[4\pm\sqrt{16-g(x)}=x\]
\[4\pm\sqrt{16-x}=g^{-1}(x)\]

Answer 8

notice how we would need to 2 functions, but of we restrict the domain to just real values 0 and above ... we get: 4+sqrt(16-x)

Answer 9

Thank you.....it took me so much time to realize what you have done....(: