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JulijaS [17]
4 years ago
14

Let f (x) =1/x

Mathematics
1 answer:
iren2701 [21]4 years ago
7 0

Answer:

The first number is 0.

The second number is 9.

Step-by-step explanation:

The circle "\circ" in f \circ g is the function composition operator. As its name suggests, it combines two functions, f and g, to give a new function.

In practice, (f\circ g)(x) is equivalent to f(g(x)). To calculate

In this case, \displaystyle f(x) = \frac{1}{x} and g(x) = x^2 - 9x.

To find an expression for (f\circ g)(x) or f(g(x)), simply replace all occurrences of x in f with g(x). That is:

(f \circ g)(x) = f(g(x)) = \displaystyle \frac{1}{g(x)}.

Since g(x) = x^2 - 9x, \displaystyle \frac{1}{g(x)} = \frac{1}{x^2 - 9x}.

Hence, \displaystyle (f \circ g) (x) = \frac{1}{x^2 - 9x}.

The expression \displaystyle (f \circ g) (x) = \frac{1}{x^2 - 9x} is undefined only when the denominator \left(x^2 - 9x\right) is equal to zero. That is: x^2 - 9x = 0.

Factor x out to obtain: x\cdot ( x - 9) = 0.

That happens either when x = 0 or when x = 9.

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