Question

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

Answer 1

F(5):

$f(5) = 3(5)^{2} - 5$

$f(5) = 15^{2} - 5$

$f(5) = 225 - 5$

$f(5) = 220$

G(5):

$g(5) = \sqrt{5} - 5 + 2$

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

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

$g(5) = -0,76$

F(4):

$f(4) = 3(4)^{2} - 5$

$f(4) = 12^{2} - 5$

$f(4) = 144 - 5$

$f(4) = 139$

G(4):

$g(4) = \sqrt{4} - 5 + 2$

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

$g(4) = -3 + 2$

$g(4) = -1$

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")

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g(x) = $\sqrt{x - 5}$ + 2

g(5) = $\sqrt{5 - 5}$ + 2  →  g(5) =  $\sqrt{0}$ + 2   →   g(5) = 2

g(4) = $\sqrt{4 - 5}$ + 2   →  g(4) =  $\sqrt{-1}$ + 2   →   g(4) = no real solutions

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