Question

Which of the following would not be a possible function for f (x) and g(x) such that f of g of x is equal to 6 over the quantity x squared end quantity plus 3
f of x is equal to 4 over x plus 2 and g(x) = x2
f of x is equal to 4 over x plus 2 and g of x is equal to 1 over the quantity x squared end quantity
f of x is equal to 4 over the quantity x squared end quantity plus 2 and g(x) = x
f of x is equal to 2 over x plus 2 and g of x is equal to x squared over 2

Answer 1

Option C is correct. the functions that would not be a possible function for f (x) and g(x) are f(x) = $\frac{4}{x^2+2}$ and g(x) = x

Given the composite function

$f(g(x))=\frac{6}{x^2+3}$

We are to look for two functions f(x) and g(x) that will not give the same function

Using trial and error,

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

Determine the f(g(x)) for this function

f(g(x)) = f(x)

This is gotten by simply replacing x with x in f(x). This will return back the function f(x) making this the right choice.

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

Since,  $\frac{4}{x^2+2}$ $\neq \frac{6}{x^2+3}$, hence the functions that would not be a possible function for f (x) and g(x) are f(x) = $\frac{4}{x^2+2}$ and g(x) = x

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