Problem: If g(x)=1βx2g(x)=1-x^{2}g(x)=1βx2 and f(g(x))=1βx2x2f(g(x))=\dfrac{1-x^{2}}{x^{2}}f(g(x))=x21βx2β when xβ 0x \neq 0xξ =0, then f(1/2)f(1 / 2)f(1/2) equals
Answer Choices:
A. 3/43 / 43/4
B. 111
C. 333
D. 2/2\sqrt{2} / 22β/2
E. 2\sqrt{2}2β Solution:
Since g(x)=1/2g(x)=1 / 2g(x)=1/2 is satisfied by x=1/2x=\sqrt{1 / 2}x=1/2β,
f(1/2)=f(g(1/2))=1f(1 / 2)=f(g(\sqrt{1 / 2}))=1f(1/2)=f(g(1/2β))=1.