Given, function f[1,∞)→[1,∞) is defined as f(x)=2x(x−1). It is an exponential function, so it is continuous and increasing in their domain. Thus, f−1 exists. Let ⇒log‌y=x(x−1)‌log‌2 ⇒(x2−x)‌log‌2−log‌y=0 ⇒x2−x−‌
log‌y
log‌2
=0 ∴‌x=‌
+1±√(−1)2−4(1)(−
log‌y
log‌2
)
2(1)
‌=‌
1±√1+4log2y
2
Here, we see that range of f(x) is [1,∞). ∵‌x=‌