Question

math problem

Answer 1

@Florisalreadytaken

Answer 2

@AZ

Answer 3

@Florisalreadytaken

Answer 4

@snowflake0531

Answer 5

what grade are you in?

Answer 6

what to do

Answer 7

do you know what f(g(x)) = x and g(f(x)) = x means? It means that f(x) and g(x) are inverses of each other

Answer 8

so there are two ways to solve for g(x), either to solve for the inverse of f(x), or to directly input g(x) into f(x)

Answer 9

Method 1: directly find the inverse
f(x) = sqrt(x+3) -9
not the standard way really but this is how I do it:
y = sqrt(x+3)-9
switch x and y
x = sqrt(y+3)-9
then put in terms of y again
sqrt(y+3) = x+9
y+3 = (x+9)^2
y = (x+9)^2 -3

Answer 10

Method two: input g(x) into f(x)
think of g(x) like x
if f(x) = 2x and g(x) = 3x, then f(g(x)) = 2(3x), where the thing in the parenthesis is whatever the input into the function f is

Answer 11

So essentially we substitute g(x) for x

Answer 12

and so f(g(x)) = x becomes
sqrt(g(x) + 3) - 9 = x
sqrt(g(x) + 3) = x + 9
g(x) + 3 = (x+9)^2
g(x) = (x+9)^2-3
which is the same answer as solving for the inverse