Question

If f(x) = (x − 3)2 + 4 and g(x) = x3 + 2, which statement is true?

(−2) = g(−3)
f(0) = g(−1)
f (8) = g(3)
f (2) = g(1)

Answer 1

Replace x in each equation with the given choices and see which one is true:

f(x) = (x − 3)2 + 4

g(x) = x3 + 2

The answer is: f (8) = g(3)

f(x) = (8-3)^2 +4 = 5^2 +4 = 25 +4 = 29

g(x) = 3^3 + 2 = 27 +2 = 29

Answer 2

f(8) = g(3)

Explanation:

f(x) = (x − 3)^2 + 4 and g(x) = x^3 + 2

We need to determine the values when we replace x

f(-2) = (-2 − 3)^2 + 4 = (-5)^2 +4 = 25+4 =29

f(0) = (0 − 3)^2 + 4 = (-3)^2 +4 = 9+4 = 13

f(2) = (2 − 3)^2 + 4 = (-1)^2 +4 = 1+4 =5

f(8) = (8 − 3)^2 + 4 = (5)^2 +4 = 25+4 =29

Now we find a g(x) value that matches one of these we are good

g(-3) =(-3)^3 + 2 = -27 +2 = -25

g(-1) = (-1)^3 + 2 = -1 +2 = 1

g(1) = (1)^3 + 2 = 1 +2 = 3

g(3) = (3)^3 + 2 = 27 +2 = 29

f(8) =29 and g(3) = 29

so f(8) = g(3)