If fog(x) = x – 3 and f(x) = x^2, what is g(x).  

Expert Answers
justaguide eNotes educator| Certified Educator

We have fog(x) = f(g(x)) = x – 3 and f(x) = x^2 and we need to determine g(x).

Let g(x) = y

=> f(y) = y  - 3 = x^2

=> x = sqrt (y – 3)

interchanging x with y gives y = g(x) = sqrt (x – 3)

Check: f(g(x)) = f( sqrt (x – 3)) = [sqrt (x – 3)]^2 = x – 3.

Therefore g(x) = sqrt (x – 3)

giorgiana1976 | Student

fog(x) = f(g(x))

If f(g(x))  =x - 3 and f(x) = x^2

f(g(x))  = (g(x))^2

But f(g(x)) = x - 3 => (g(x))^2  =x - 3

To determine g(x), we'll apply square root both sides:

sqrt(g(x))^2 = sqrt(x-3)

g(x) = sqrt(x-3)