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}# ?

1 Answer
Kalit Gautam
Feb 24, 2018

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 :-

GeoGebra Classic app

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