Answer: (-3x + 28)/(24 - 7x).
Step-by-step explanation: To find f composed with f of x, we need to substitute the expression f(x) into itself and simplify.
Given:
f(x) = (x - 4)/(x - 8)
1. Substitute f(x) into itself:
f(f(x)) = f((x - 4)/(x - 8))
2. Simplify the expression:
To simplify, we substitute the expression (x - 4)/(x - 8) into f(x).
f(f(x)) = [(x - 4)/(x - 8) - 4]/[(x - 4)/(x - 8) - 8]
3. Simplify further:
To simplify this expression, we need to find a common denominator for both fractions.
f(f(x)) = [(x - 4 - 4(x - 8))/(x - 8)] / [(x - 4 - 8(x - 4))/(x - 8)]
Expanding the numerator and denominator:
f(f(x)) = [(x - 4 - 4x + 32)/(x - 8)] / [(x - 4 - 8x + 32)/(x - 8)]
Simplifying the numerator and denominator:
f(f(x)) = [(-3x + 28)/(x - 8)] / [(24 - 7x)/(x - 8)]
4. Divide the fractions:
To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.
f(f(x)) = [(-3x + 28)/(x - 8)] * [(x - 8)/(24 - 7x)]
Cancelling out the common factor (x - 8):
f(f(x)) = (-3x + 28)/(24 - 7x)
Therefore, f composed with f of x is given by the expression (-3x + 28)/(24 - 7x).
SEEE :)