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


y = Seven divided by x squared. + 10

Please give a detailed explanation to this question and I will mark your answer the brainliest answer

Respuesta :

nadiroz
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

Answer:

[tex]f(x)= \frac{7}{x}+10[/tex] and [tex]g(x)=x^2[/tex] 

Step-by-step explanation:

Given : Equation [tex]y=\frac{7}{x^2}+10[/tex].

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,

[tex]y= \frac{7}{x^{2}}+10[/tex]

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

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

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

Therefore, [tex]f(x)= \frac{7}{x}+10[/tex] and [tex]g(x)=x^2[/tex].

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