Suppose f(x)= sqrt x^2+2x+8 and g(x)= 4x+2
simplify this equation:
(f of g)(x)=
(f of g)(-3)=
To find (f of g)(x), we need to substitute g(x) into f(x) and simplify the resulting equation.
(f of g)(x) = f(g(x))
(f of g)(x) = f(4x+2)
(f of g)(x) = sqrt((4x+2)^2 + 2(4x+2) + 8)
(f of g)(x) = sqrt(16x^2 + 16x + 4 + 8x + 4 + 8)
(f of g)(x) = sqrt(16x^2 + 24x + 16)
Therefore, (f of g)(x) = sqrt(16x^2 + 24x + 16).
To find (f of g)(-3), substitute x = -3 into the equation we found:
(f of g)(-3) = sqrt(16*(-3)^2 + 24*(-3) + 16)
(f of g)(-3) = sqrt(16*9 - 72 + 16)
(f of g)(-3) = sqrt(144 - 72 + 16)
(f of g)(-3) = sqrt(88)
Therefore, (f of g)(-3) = sqrt(88).