Question

For f(x)=1/x^2-3, find
a) f(3)
b) f(2+h)
Show/explain work

Answer 1

`f(x)=(1)/(x^2-3)\\\\a)\ f(3)\to\text{put x=3 to the equation of the function f}\\\\f(3)=(1)/(3^2-3)=(1)/(9-3)=(1)/(6)\\\\Answer:\ \boxed{f(3)=(1)/(6)}\\\\b)\ f(2+h)\to\text{put x=2+h to the equation of a function f}\\\\f(2+h)=(1)/((2+h)^2-3)\ \ \ |\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=(1)/(2^2+2(2)(h)+h^2-3)=(1)/(4+4h+h^2-3)=(1)/(h^2+4h+1)\\\\Answer:\ \boxed{f(2+h)=(1)/(h^2+4h+1)}`