Question

What are the domain and range of f(x)=(1/5)^x

Answer 1

You should graph the function to help find domain and range.

The domain stands for the values that x can have in the equation.  In this equation any real number can be substituted for x so the answer the domain is (-∞, ∞).

Range stands for the values that y can have in the equation.  You can see from the graph that the graph never has a negative y value, so the range is (0, ∞).

Answer 2

Answer: The domain of the function is all real numbers $(-\infty,\infty)$ and the range is all positive real numbers  $(0,\infty)$.

Explanation:

The given function is,

$f(x)=(\frac{1}{5} )^x$

The set of all possible values of x for which f(x) is defined is called domain of the function f(x).

The given function is defined on all real values therefore the domain of the given function is all real numbers.

$Domain=(-\infty,\infty)$

The set of all values of f(x) at different value of x is called range of the function f(x).

Since the given function is in the form of,$f(x)=a^x$, where the value of a is less than 1 and more that 0. It means as the power approaches to a large number the value of f(x) approaches towards 0. As the power approaches to a negative large number the value of f(x) approaches towards infinity.

The value of function is always positive but not equal to 0.

$Range=(0,\infty)$

Therefore, the domain is $(-\infty,\infty)$ and the range is $(0,\infty)$.

The graph of f(x) is above the y-axis, therefore the range is $(0,\infty)$.