Question

The range of the function given below is the set of all positive real numbers greater than 5

f(x)=5+4^x
true or false?

Answer 1

True

Explanation:

just did it

Answer 2

True -
`R=(5,\infty) , y|y>5`

Explanation:

Given : The range of the function given below is the set of all positive real numbers greater than 5 ,
`f(x)=5+4^x`

To find : The given statement is true or false?

Solution :

Domain of the function is where the function is defined

The given function
`f(x)=5+4^x` is an exponential function

So, the domain of the function is,

`D=(-\infty,\infty) , x|x\in \mathbb{R}`

i.e, The set of all real numbers.

Range is the set of value that corresponds to the domain.

Let
`y=5+4^x`

If
`x\rightarrow \infty , y\rightarrow 5`

If
`x\rightarrow -\infty , y\rightarrow \infty`

So, The range of the function is

`R=(5,\infty) , y|y>5`

Therefore, The given statement is true.