Suppose f(x)= sqrt x^2+5x+8 and g(x)= 8x-6

Question

(f of g)(x)= don't simplify this equation

(f of g)(-4)=

Answer 1

(f of g)(x) = f(g(x))

Substitute g(x) into f(x)

(f of g)(x) = sqrt((8x-6)^2 + 5(8x-6) + 8)

(f of g)(x) = sqrt(64x^2 - 96x + 36 + 40x - 30 + 8)

(f of g)(x) = sqrt(64x^2 - 56x + 14)

Now, to find (f of g)(-4), substitute x = -4 into the equation:

(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 + 238)
(f of g)(-4) = sqrt(1262) or approximately 35.52