Question

Which of the following is true with respect to the following functions: *photo*

Answer 1

In order to find the correct option, let's analyze each one:

A.

To check this option, let's find the inverse function of h(x):

`\begin{gathered} h(x)=3^x+1\\ \\ x=3^(f(x))+1\\ \\ 3^(f(x))=x-1\\ \\ \log_33^(f(x))=\log_3(x-1)\\ \\ f(x)=\log_3(x-1) \end{gathered}`

We can see that f(x) is not equal to i(x), so this option is false.

B.

i(x) is a logarithm function, which grows slowly. Function h(x) is an exponential function and it grows the fastest.

C.

g(x) is a polynomial function and h(x) is an exponential function. These functions have as domain all real numbers. Then, the option says h(x) also has a restricted domain, which is false.

D.

The range of i(x) is all real numbers, while the range of the other functions is mostly positive values.

Therefore the correct option is D.