Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point)

Answer 1

Answer:

$f(x)= \frac{7}{x}+10$ and $g(x)=x^2$ 

Step-by-step explanation:

Given : Equation $y=\frac{7}{x^2}+10$.

To find : f(x) and g(x) so the function can be expressed as y = f(g(x)) ?

Solution :

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

In the expression,

$y= \frac{7}{x^{2}}+10$

We may notice two functions, the squaring x function, which may well be our g i.e. $g(x)=x^2$ 

The function is re-written as, $y= \frac{7}{g(x)}+10$

and the "7 divided by x, +10" function is  $f(x)= \frac{7}{x}+10$

Therefore, $f(x)= \frac{7}{x}+10$ and $g(x)=x^2$.

Answer 2

Given y = 7/x² + 10

Let,

y = f(x)

f(x) = 7/x² + 10

And,

g(x) = x²

Hence, f(g(x))

Reason is;
You have to rewrite f(x) so that it can fit in g(x) into the equation

f(x) = 7/g(x) + 10