Math Question?

Question

Consider the functions f(x)=3xsquared-5 and g(x)squareroot x-5+2.

A. Find f(5)
B. Find f(4)
C. Find g(5)
D. Find g(4)
E. Describe the domain of f(x).
F. Describe the domain of g(x).
G. What is it about the functions f(x) and g(x) that causes one domain to be more restrictive than the other?

Answer 1

f(5) = 3*5^2 - 5 = 70
f(4) = 3*4^2 - 5 = 43
g(5) = sqrt(5-5) +2 = 2
g(4) = sqrt(4-5) + 2 = 2+i
Domain of f(x) is all the real numbers
Domain of G(x) is x>=5
The square root of a negative number is imaginary and not part of the real numbers,

Answer 2

E. For f(x), since x is being squared, you may substitute ANY NUMBER for x, because you can square any number. The domain of f(x) is ALL REAL NUMBERS

F. For g(x), you have the square root of (x - 5). Just remember that you cannot take the square root of a negative number. So the quantity (x - 5) must be either zero or a positive number. So solve the following equation to get your domain.

x - 5 >= 0
x >= 5

The domain of g(x) is all real numbers such that x is greater than or equal to five.

Answer 3

a) f(5) = 70
b) 43
c) taking g(x) = (x-5)^1/2 + 2
2
d) 2 + i
e) (-oo,oo)
f) [5,oo)
g) there cannot be a negative number in the radical of g(x)