Question

How do you do this?

A. Domain: all real numbers; Range: all real numbers

B. Domain: all real numbers; Range: y>2

C. Domain: all real numbers; Range: y>0

D. Domain:x<1; Range: y>2

E. Domain: x<1; Range: all real numbers

Answer 1

Answer is option `B` i.e. Domain: all real numbers; Range: `y>2`

Explanation:

As `f(x)=5(4)^x+2`

`x` can take any value from `-oo` and `oo` and hence domain is all real numbers.

As `x->-oo`, `f(x)=5(4)^(-oo)+2=5/4^oo+2=0+2`, hence `f(x)->2` and hence minimum value of `f(x)` is `2`

and when `x->oo` `f(x)->oo`

Hence range is `y>2`

and answer is option `B` i.e. Domain: all real numbers; Range: `y>2`