Suppose f(x)= sqrt x^2+5x+8 and g(x)= 8x-6
simplify this equation (f of g)(x)=
(f of g)(-4)=
To find (f of g)(x), we first plug in g(x) into f(x):
f(g(x)) = sqrt((8x-6)^2 + 5(8x-6) + 8)
f(g(x)) = sqrt(64x^2 - 96x + 36 + 40x - 30 + 8)
f(g(x)) = sqrt(64x^2 - 56x + 14)
Now to evaluate (f of g)(-4), we substitute x = -4:
(f of g)(-4) = sqrt(64(-4)^2 - 56(-4) + 14)
(f of g)(-4) = sqrt(64(16) + 224 + 14)
(f of g)(-4) = sqrt(1024 + 224 + 14)
(f of g)(-4) = sqrt(1262)
(f of g)(-4) ≈ 35.52
Therefore, (f of g)(-4) is approximately 35.52.