Question

How do you find the range from an undefined graph?

The function: `f(x)= log(x^2 +6x +9)` has a point of (`-3`, undefined) in its graph. How do you find the range?

Is the domain `{xeR}` ?

Answer 1

The domain of this function is `D_f : x ∈R-{-3}` The range of this function is `R_f : f(x) ∈ (-∞,∞)`

Explanation:

We can see that the the function `g(x)=(x^2 + 6x + 9 )` attains all the values from `(0,∞)` which is the Domain for the outer logarithmic function, thus it attains all the values which are attained by the function `f(x) = log_10x`.

The Range of `g(x)` acts as the Domain of `f(x)`.

`:. R_f : f(x) ∈ (-∞,∞)`

The graph of the function `f(x)` is given below :-