Question

Consider the functions f(x)=3x^2 - 5 and g(x)= √x -5 +2

how can i find
f(5)
g(5)
f(4)
g(4)
describe the domain of f(x)
describe the domain of g(x)
why is the domain of one of these functions more restructive than the other?

Answer 1

F(5):

`f(5) = 3(5)^(2) - 5`

`f(5) = 15^(2) - 5`

`f(5) = 225 - 5`

`f(5) = 220`

G(5):

`g(5) = √(5) - 5 + 2`

`g(5) = 2,24 - 5 + 2`

`g(5) = -2,76 + 2`

`g(5) = -0,76`

F(4):

`f(4) = 3(4)^(2) - 5`

`f(4) = 12^(2) - 5`

`f(4) = 144 - 5`

`f(4) = 139`

G(4):

`g(4) = √(4) - 5 + 2`

`g(4) = 2 - 5 + 2`

`g(4) = -3 + 2`

`g(4) = -1`

Hope it helped,

BioTeacher101

Answer 2

f(x) = 3x² - 5

f(5) = 3(5)² - 5 → f(5) = 3(25) - 5 → f(5) = 75 - 5 → f(5) = 70

f(4) = 3(4)² - 5 → f(4) = 3(16) - 5 → f(4) = 48 - 5 → f(5) = 43

DOMAIN of f(x): All real numbers (because there are no restrictions on "x")

************************************************************

g(x) =
`√(x - 5)` + 2

g(5) =
`√(5 - 5)` + 2 → g(5) =
`√(0)` + 2 → g(5) = 2

g(4) =
`√(4 - 5)` + 2 → g(4) =
`√(-1)` + 2 → g(4) = no real solutions

DOMAIN of g(x): x ≥ 5 (because you cannot take the square root of a negative number)