Answer:
The answer is below⬇️⬇️
Step-by-step explanation:
f(x) = 3x+4
g(x) = 2x
h(x) = x²+x-2
g(hx) = 2(x²+x-2)
= 2x²+2x-4
f(g(hx))=3(2x²+2x-4)+4
=6x²+6x-12+4
=6x²+6x-8
g(f(g(hx)))=2(6x²+6x-8)
=12x²+12x-16
f(g(f(g(hx))))=3(12x²+12x-16)+4
=36x²+36x-48+4
=36x²+36x-44
h(f(g(f(g(hx)))))=(36x²+36x-44)²+36x²+36x-44-2
=1296x⁴+2592x³-1872x²-3168x+1936+36x²+36x-46
=1296x⁴+2592x³-1836x²-3132x+1890
f(h(f(g(f(g(hx))))))=3(1296x⁴+2592x³-1836x²-3132x+1890)+4
=3888x⁴+7776x³-5508x²-9396x+5674
h(f(h(f(g(f(g(hx)))))))=(3888x⁴+7776x³-5508x²-9396x+5674)²+3888x⁴+7776x³-5508x²-9396x+5674-2
=15116544x⁸+60466176x⁷+17635968x⁶-158723712x⁵-71663616x⁴+657591048x³-255531048x²-106635204x+32194276
