Mark the correct alternative in each of the following:
Let [x] denote the greatest integer less than or equal to x. If f(x) = sin–1 x, g(x) = [x2] and then
Given that f(x) = sin–1 x, g(x) = [x2] and
a. goh(x) = g(2x)
⇒ goh(x) = [4x2]
fogoh(x) = f([4x2])
⇒ fogoh(x) = sin–1 [4x2]
Hence, given option is incorrect.
b. Similarly, this option is also incorrect.
c. fog(x) = f([x2])
⇒ fog(x) = sin–1 [x2]
hofog(x) = h(sin–1 [x2])
⇒ hofog(x) = 2(sin–1 [x2])
gof(x) = g(sin–1 x)
⇒ gof(x) = [(sin–1 x)2]
hogof(x) = h([(sin–1 x)2])
⇒ hogof(x) = 2[(sin–1 x)2]
Hence, hogof(x) ≠ hofog(x)