Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)).

y = two divided by x squared + 9

Answer 1

can you write the equation of y in mathematical form?

Answer 2

y= 2\[y=2/x^2+9\]

Answer 3

so when the value of g(x) is input into f(x) the following equation occurs
lets says g(x) =x
so if f(x) = 2/x +9 our following equation of y can occur.

Answer 4

\[1. y=\frac{ 2 }{ x^{2}}+9\]
OR
\[2. y=\left( \frac{ 2 }{ x } \right)^{2}+9\]

Answer 5

1

Answer 6

Or ....

I read it as y = 2 / (x^2 + 9)

f(x) = 2 / x g(x) = x^2 + 9

y = f(g(x))

y = 2 / g(x)

y = 2 / (x^2 + 9)

Parenthesis make a difference, so I am most likely incorrect.

Answer 7

@hamza123: Please defend your first statement. I don't agree with your "f(x)." Please use the notation f(x) and g(x), not y and y, to eliminate ambiguity.

Answer 8

Both f(x) and g(x) must be functions that have at least one occurrence of the variable x.
Otherwise, you cannot use g(x) as the input to f(x).

@hamza123: Please re-write your initial "y=2." As now written, it's not complete.