Mister Exam
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-
How to use it?
- Graphing y =:
- 1/(x^2+5x-6)
- x+arctgx
- -x/2
- x^2*e
- Derivative of:
-
-log(x-1)
-
Identical expressions
- -log(x- one)
- minus logarithm of (x minus 1)
- minus logarithm of (x minus one)
- -logx-1
-
Similar expressions
- sqrt(x-log(x)-1)^(3)
- sqrt(2)*sqrt(1/(x-log(x)))*(-1+x)/2
- log(x-1)
- -(log((x-1))/log((3/10)))/sqrt(-x^2+2*x+8)
- -log(x+1)
- sqrt(2-(log(x-1)/log(2))^2)
Graphing y = -log(x-1)
The solution
You have entered
[src]
f(x) = -log(x - 1)
$$f{\left(x \right)} = - \log{\left(x - 1 \right)}$$
f = -log(x - 1)
The graph of the function
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$- \log{\left(x - 1 \right)} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 2$$
Numerical solution
$$x_{1} = 2$$
so we need to solve the equation:
$$- \log{\left(x - 1 \right)} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 2$$
Numerical solution
$$x_{1} = 2$$
Extrema of the function
In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$- \frac{1}{x - 1} = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$- \frac{1}{x - 1} = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$\frac{1}{\left(x - 1\right)^{2}} = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$\frac{1}{\left(x - 1\right)^{2}} = 0$$
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty}\left(- \log{\left(x - 1 \right)}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(- \log{\left(x - 1 \right)}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(- \log{\left(x - 1 \right)}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(- \log{\left(x - 1 \right)}\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of -log(x - 1), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(- \frac{\log{\left(x - 1 \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(- \frac{\log{\left(x - 1 \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{x \to -\infty}\left(- \frac{\log{\left(x - 1 \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(- \frac{\log{\left(x - 1 \right)}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
$$- \log{\left(x - 1 \right)} = - \log{\left(- x - 1 \right)}$$
- No
$$- \log{\left(x - 1 \right)} = \log{\left(- x - 1 \right)}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$- \log{\left(x - 1 \right)} = - \log{\left(- x - 1 \right)}$$
- No
$$- \log{\left(x - 1 \right)} = \log{\left(- x - 1 \right)}$$
- No
so, the function
not is
neither even, nor odd