Determine if the subset of cinfinty inifiny is a subspace of

Determine if the subset of c(-infinty, inifiny) is a subspace of c(-infinty, inifiny)

26. the set of all exponential function f(x)=a^x where a>0

Chegg says it\'s a subspace, but I am not fully convinced

in order to have s subspace

* it should contain the zero vector

* it should be closed under adition

* it should be closed under multipilcation

I think we can\'t mulitpy a by a negative scalar

Can somebody helps me on this one?

I\'m totally agree with you that we are not getting zero vector.

Because a>0 will always give positive value for any x positive or negative. so a^x will not generate negative value.

Obviously sum of two positive values is again positive so we will not get zero vector.