Question

F(x)= 6x³-9x²+18x-18÷7x³-8x²+3x-20
What is the value of f (3)

Answer 1

`(117)/(106)`

Explanation:

given

`f(x)=(6x^3-9x^2+18x-18)/(7x^3-8x^2+3x-20)`,

we are to find the value of
`f(3).` we substitute
`x=3` and find the value of the rational function.

`f(3)=(6(3)^3-9(2)^2+18(3)-18)/(7(3)^3-8(3)^2+3(3)-20)`

now we evaluate.

`(6(3)^3-9(3)^2+18(3)-18)/(7(3)^3-8(3)^2+3(3)-20)=(6(27)-9(9)+18(3)-18)/(7(27)-8(9)+3(3)-20)`
`\implies (162-81+54-18)/(189-72+9-20)`

`\implies (117)/(106)`.

Answer 2

`\sf f(3) = (117)/(106)`

Explanation:

To find the value of
`\sf f(3)` for the given function:

`\sf f(x) = (6x^3 - 9x^2 + 18x - 18)/(7x^3 - 8x^2 + 3x - 20)`

Simply substitute
`\sf x = 3` into the function:

`\sf f(3) = (6(3)^3 - 9(3)^2 + 18(3) - 18)/(7(3)^3 - 8(3)^2 + 3(3) - 20)`

Now, calculate the numerator and denominator separately and then divide:

`\sf f(3) = (6(27) - 9(9) + 18(3) - 18)/(7(27) - 8(9) + 3(3) - 20)`

`\sf f(3) = (162 - 81 + 54 - 18)/(189 - 72 + 9 - 20)`

`\sf f(3) = (117)/(106)`

So,
`\sf f(3) = (117)/(106)`.