What is the domain and range of this function?

1 answer:

max2010maxim [7]2 years ago

5 0

As for the domain, the only restriction comes from the logarithm. The argument of a logarith must be strictly positive, so we have

$x-2>0 \iff x>2$

As for the range, we have:

The range of $\log(x)$ are all real numbers
If we change to $\log(x-2)$ we're translating the function horizontally, so the range remains the same
If we change to $\log(5(x-2()$ we're stretching the function horizontally, so the range doesn't change
If we change to $\log(5(x-2))+1$ we're translating the function 1 unit up, but the range is already all the real numbers, so it doesn't change.

You might be interested in

Simplify the following expression:

Phantasy [73]

$\frac{4}{ \frac{1}{4} - \frac{5}{2} }$

To begin, we can simplify the expression's denominator by finding a common denominator between the denominators of the fractions in the denominator. To make them compatible, we can convert $\frac{5}{2}$ into $\frac{10}{4}$ :

$\frac{4}{ \frac{1}{4} - \frac{5}{2}( \frac{2}{2}) } = \frac{4}{ \frac{1}{4} - \frac{10}{4} }$

Next, we can simplify:

$\frac{4}{ \frac{1}{4} - \frac{10}{4} } = \frac{4}{ -\frac{9}{4}}$

Finally, to cancel the denominator within the denominator, we can multiply the whole expression by $\frac{4}{4}$ , or 1:

$\frac{4}{ -\frac{9}{4}}* \frac{4}{4} = -\frac{16}{9}$

The expression simplifies to $-\frac{16}{9}$ , or $-1 \frac{7}{9}$ as a mixed number.