Question

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

y= 8/sqareroot of 2x+4
f(x) = 8, g(x) = square root of quantity two x plus four.
f(x) = square root of quantity two x plus four., g(x) = 8
f(x) = eight divided by x., g(x) = 2x + 4
f(x) = eight divided by square root of x., g(x) = 2x + 4

Answer 1

The fourth option gives the result.

Explanation:

We have to find f(x) and g(x) from options given such that y = f[g(x)] is equivalent to
`y = (8)/(√(2x + 4))`.

Here, the fourth option gives the result.

If
`f(x) = (8)/(√(x) )` and g(x) = 2x + 4, then the composite function
`f[g(x)] = (8)/(√(2x + 4))`

⇒
`y = (8)/(√(2x + 4))` ( Answer )