Question

For the functions f(x) =x+2 and g(x)=x^2 -3 which expression has the greatest value?

f(g(1))
f(g(-2))
g(f(-4)
g(f(-2))

Answer 1

f(g(-2))

Explanation:

f(x) =x+2 and g(x) = x² -3

start working from inside towards outside

f(g(1)) = f(1² -3) = f(-2) = -2+2 = 0

f(g(-2)) = f((-2)² -3) = f(4-3)= f(1) = 1+2 = 3

g(f(-4) = g(-4+2) = g(-2) = (-2)² -3 = 4-3 = 1

g(f(-2)) = g(-2+2) = g(0) = 0² -3 = 0-3 = -3

The expression with the greatest value is f(g(-2))

because equals 3 ( 3>0, or 1, or -3)