Question

What is the solution to this equation?? Please explain steps

Let f(x)=`x^2+7` and g(x)= `(x-3)/x`
Find `(f@g)(-3)`

Answer 1

11

Explanation:

The `@` notation is to indicate compound functions. Specifically, `f@g(x) = f(g(x))`. To evaluate this, you sub in the value of g(x) into f(x).

`f@g(-3) = f(g(-3)) = f((-3-3)/-3) = f(2) = 2^2 + 7 = 11`

Another method to do this is to evaluate the compound function directly, and substitute in the value of -3.

`f@g(x) = f(g(x)) = f((x-3)/x) = ((x-3)/x)^2 + 7`.

`f@g(-3) = ((-3-3)/-3)^2 + 7 = 11`