Question

find the range of the function f(x)=4^x+2^x+1​

Answer 1

Answer:

The range of the function is (1,∞).

Step-by-step explanation:

Consider the provided function.

$f(x)=4^x+2^x+1​$

The Range of the function is the set of output values which a function can produced or the set of y values.

Here, if we observe the function we can see that no value of x can produced a negative y value.

For example:

The reason is, if we substitute x = -1 the function will look like:

$f(x)=4^(-1)+2^(-1)+1​$

$f(x)=\frac{1}{4}+\frac{1}{2}+1​$

Which is going to be a positive value and more than 1. The range of this function contains only positive number.

Therefore, if x approaches to -∞ then the value of function move towards 1. as 1 is the constant and if we add any positive number, we always get a number greater than 1.

The graph of the function is shown in figure 1:

Thus, the range of the function is 1 to ∞, in interval notation (1,∞).