Get the answer to "An expression for f(x) and g(x):" - Plainmath

Khadija Wells

Answered question

2021-09-18

An expression for f(x) and g(x):

Answer & Explanation

firmablogF Skilled2021-09-19Added 92 answers

We can define composite functions as follows

(f \cdot g) (x) = f (g (x))

(g \cdot f) (x) = g (f (x))

Calculation:
Since

h (x) = (g \cdot f) (x)

Therefore

(g \cdot f) (x) = \frac{1}{{(x - 1)}^{2}}

g (f (x)) = \frac{1}{{(x - 1)}^{2}}

So, we can assume,

f (x) = x - 1

and

g (x) = \frac{1}{x^{2}}

Conclusion:

f (x) = x - 1

g (x) = \frac{1}{x^{2}}

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