If g(x)>0 for all real values of x, which of the following could be function g?

a) g(x)= x+1
b) g(x)=x-1
c) g(x)= x^2+1
d) g(x) = x^2-1
e) g(x) = x^3 + 1

To find out which function g(x) could be, we need to determine which of the given functions are always positive for all real values of x.

Let's analyze each function:

a) g(x)= x+1
We can see that g(x) will not always be positive since x can take on negative values, making the expression x+1 negative.

b) g(x)=x-1
Similar to the previous function, g(x) will not always be positive because x can take on negative values, making the expression x-1 negative.

c) g(x)= x^2+1
In this case, g(x) will always be positive because taking the square of any number will result in a non-negative value, and adding 1 ensures that g(x) is greater than 0.

d) g(x) = x^2-1
Like the previous function, g(x) will not always be positive because when x is 0, the expression x^2-1 equals -1.

e) g(x) = x^3 + 1
Similar to the other functions, g(x) will not always be positive since x can take on negative values, making the expression x^3+1 negative.

Based on this analysis, the only function that could be g(x) is c) g(x) = x^2+1, since it is positive for all values of x.