Question

If f(x)=1/x+2 what is f(3+h)?

Answer 1

If x is the only thing in the denominator, then,

`f(x) = (1)/(x)+2\\\\f(3+h) = (1)/(3+h)+2\\\\f(3+h) = (1)/(3+h)+2\left((3+h)/(3+h)\right)\\\\f(3+h) = (1+2(3+h))/(3+h)\\\\f(3+h) = (1+6+2h)/(3+h)\\\\f(3+h) = (7+2h)/(3+h)\\\\`

We replace every copy of x with 3+h, as shown in the second step. Afterwards, we can optionally simplify to form one big fraction.

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Or if the "x+2" is in the denominator, then we have these steps:

`f(x) = (1)/(x+2)\\\\f(3+h) = (1)/(3+h+2)\\\\f(3+h) = (1)/(h+5)\\\\`