What is the domain of defination of y= log_10 (1- log_10 (x^2 -5x +16))?
If possible ,please solve without using limits.
If possible ,please solve without using limits.
1 Answer
May 31, 2017
The domain is the interval
Explanation:
Given:
y = log_10(1-log_10(x^2-5x+16))
Assume that we want to deal with this as a real valued function of real numbers.
Then
Note that:
x^2-5x+16 = (x-5/2)^2+39/4 > 0
for all real values of
So:
log_10(x^2-5x+16)
is well defined for all real values of
In order that
1 - log_10(x^2-5x+16) > 0
Hence:
log_10(x^2-5x+16) < 1
Taking exponents of both sides (a monotonically increasing function) we get:
x^2-5x+16 < 10
That is:
x^2-5x+6 < 0
which factors as:
(x-2)(x-3) < 0
The left hand side is
So the domain is