Function Problem Help Please?

Question

Let the function h be defined by h(x) = 14 + x^2 / 4 . If h(2m) = 9m, what is one possible value of m?


The answer is supposed to be either 2 or 7, but i can't seem to come to those answers. Please give me a step by step of how to get to those. Thanks alot

Answer 1

It is not that difficult.
Look:

h(x) = 14 + x^2 / 4

then h(2m) = 14 + (2m)^2 / 4
h(2m) = 14 + 4m^2 / 4
n(2m) = 9m ===> 14 + 4m^2 / 4 = 9m multiply both sides by 4
56 + 4m^2 = 36m
4m^2 - 36m + 56 = 0
m^2 - 9m + 14 = 0
(m - 2)(m - 7) = 0
m = 2 or m = 7

Good Luck,

Kempos

Answer 2

h(2m) means that for every "x" variable you replace it with 2m. Since you know that h(2m) = 9m you can set up an equation like the following: 9m = 14 + (2m)^2 / 4

9m = 14 + 4m^2 / 4
9m = 14 + m^2
m^2 - 9m + 14 = 0
now it's just a simple step of foiling/factoring

(m-2)(m-7)
So you get that m equals 2 or 7

Answer 3

h(2m) = 14 + (2m)^2 + 9 m
simplifies to m^2 - 9m _ 14 = 0
solve the equation and you get m = 2 or 7.

Answer 4

h(2m) means you substitute in the value 2m into the equation whever we see the variable.

So, 14 + (2m)^2 / 4 = 9m

14 + 4m^2 / 4 = 9m
14 + m^2 = 9m
14 + m^2 - 9m = 0
m^2 - 9m + 14 = 0
(m - 2) (m - 7) = 0

m - 2 = 0 or m - 7 = 0
m = 2 or m = 7

Answer 5

h(2m) = 9m
14 + (2m)²/4 = 9m
14 + 4m²/4 = 9m
14 + m² = 9m
m² - 9m + 14 = 0
(m - 7)(m - 2) = 0
m = 7 or m = 2

=)