for f(x)= 1/(x^2-3), find:
a. f(3)
b.f(2+h)
a.
Replace x with 3
f ( 3 )= 1 / ( x ^ 2 - 3 ) =
1 / ( 3 ^ 2 - 3 ) =
1 / ( 9 - 3 ) = 1 / 6
b.
Replace x with 2 + h
f ( 2 + h )= 1 / [ ( 2 + h ) ^ 2 - 3 ] =
1 / ( 2 ^ 2 + 2 * 2 * h + h ^ 2 - 3 ) =
1 / ( 4 + 4 h + h ^ 2 - 3 ) =
1 / ( h ^ 2 + 4 h + 1 )
oh! thank you, you made it very understanding
You're welcome.
To find the values of the function f(x) = 1/(x^2 - 3), we can substitute the given values into the function expression.
a. To find f(3), substitute x = 3 into the function f(x):
f(x) = 1/(x^2 - 3)
f(3) = 1/(3^2 - 3)
= 1/(9 - 3)
= 1/6
Therefore, f(3) = 1/6.
b. To find f(2 + h), substitute x = 2 + h into the function f(x):
f(x) = 1/(x^2 - 3)
f(2 + h) = 1/((2 + h)^2 - 3)
We can simplify further by expanding the square term:
f(2 + h) = 1/((4 + 4h + h^2) - 3)
= 1/(h^2 + 4h + 1)
So, f(2 + h) = 1/(h^2 + 4h + 1).