Let fx 21nx gx e2x 3 hx 2x find f degree g degree h 2 10

Let f(x) = -21n(x), g(x) = e^2x + 3, h(x) = -2^x; find (f degree g degree h) (2) -10 10 22 -22 -16 None of the above

Solution

fogoh(x) = f(g(h(x)))

h(x) = -2^x

g(h(x)) = e^(-2*2^x + 3) = e^(-2^(x+1) + 3)

f(g(h(x))) = -2*ln [e^(-2^(x+1) + 3)]

= -2*(-2^(x+1) + 3)

f(g(h(x))) = 2^(x + 2) - 6

f(g(h(2))) = 2^(2 + 2) - 6 = 16 - 6 = 10

Correct option is B.