Answer:
(f º f)(3) = 30, when f(x) = x² - x
Step-by-step explanation:
This is a great example of composite functions and how to multiply one function by another. (f º f) really means f(f(x)), or replacing every x in the original function f(x) with the function f(x).
Step 1: State the original function.
[tex]f(x) = x^{2} -x[/tex]
Step 2: Insert the function f(x) wherever there is an x.
[tex]f(f(x))=(x^{2} -x)^{2} -(x^2-x)[/tex]
Step 3: Expand anything that has an exponent. Remember: [tex](x+y)^2 = (x+y)(x+y)[/tex]
[tex]f(f(x))=(x^{2} -x)(x^{2} -x) -(x^2-x)[/tex]
Step 4: Foil the parts of the equations in brackets by multiplying the first terms, outside terms, inside terms and last terms in each bracket.
[tex]f(f(x))=(x^{4}-x^3-x^3+x^{2}) -(x^2-x)[/tex]
Step 5: Now you can remove the brackets (don'f forget to switch the symbols for the second brackets because you are subtracting) and sum the like terms.
[tex]f(f(x))=x^{4}-x^3-x^3+x^{2} -x^2+x[/tex]
[tex]f(f(x))=x^{4}-2x^3+x[/tex]
Step 6: Finally, substitute the given x value, which is 3, into the new equation.
[tex]f(f(x))=(3)^{4}-2(3)^3+(3)[/tex]
[tex]f(f(x))=81-54+3[/tex]
[tex]f(f(x))=30[/tex]
Therefore the answer is (f º f)(3) = 30.
Answer:
30
Step-by-step explanation:
Method 1:
ƒ(x) = x² - x
(f∘f)(x) = f(f(x)) = f(x²-x) = (x² - x)² - (x² - x) = x⁴ - 2x³ + x² - x² + x = x⁴ - 2x³ + x
(f∘f)(3) = 3⁴ - 2(3)³ + 3 = 81 - 54 + 3 = 30
Method 2:
f(3) = 3² - 3 = 9 - 3 = 6
(f∘f)(3) = f(f(3)) = f(6) = 6² - 6 = 36 - 6 = 30
