Soal fungsi g(x) = 1/x2+1 , (fog)(x) = -2x2-1/x2+1 , maka f(x) adalah

fog(x) = -2x²+1 / x²+1
f(1 / x²+1) = -2x²-1 / x²+1
misalkan p = 1 / x²+1
x² + 1 = 1/p
x² = 1/p - 1
x² = (1 - p)/p
x = √{(1-p)/p}
f(p) = -2{√(1-p)/p}²-1 / {√(1-p)/p}²+1
f(p) = -2{(1-p)/p}-1 / {(1-p)/p}+1
= {(-2+2p)/p - 1} / {(1-p)/p + 1}
= {(-2+2p)/p - p/p} / {(1-p)/p + p/p}
= (-2+2p-p)/p / (1-p+p)/p
= (-2+p)/p / (1/p)
= (-2+p)/p × (p/1)
= -2 + p
f(x) = -2 + x
atau
f(x) = x - 2