Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)). y = (8/x^2) + 4

Answer 1

y=f(g(x))      and      $y= \frac{8}{x^{2}}+4$


our aim is to express f as a function of g, where g is a function itself, of x.

in the expression tex]y= \frac{8}{x^{2}}+4 [/tex] we may notice 2 functions:

the squaring x function, which may well be our g: $g(x)= x^{2}$

and the "8 divided by x, +4" function: $f(x)= \frac{8}{x}+4$


check : 

$f(g(x))= \frac{8}{g(x)}+4$

because whatever the input of f is, it divides it from 8, and adds 4 to the division. 

since, $g(x)= x^{2}$, 

$f(g(x))= \frac{8}{g(x)}+4=\frac{8}{x^{2}}+4$


Answer:

$g(x)= x^{2}$

$f(x)= \frac{8}{x}+4$