If f: R—>R,f(x)=x— [x], then f⁻¹(x)=.........,Select Proper option from the given options.
(a) does not exist
(b) is x
(c) is [x]
(d) x-[x]
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f : R -------> R , f(x) = x - [x] is a fractional function. where [x] denotes greatest integer.
f(x) = x - [x] also written as {x} ,range of fractional part of x is 0 ≤ x < 1.
if we take two different values of x
e.g., -0.5 and 0.5
then, f(-0.5) = -0.5 - [-0.5] = -0.5 -(-1) = 0.5
f(0.5) = 0.5 - [0.5 ] = 0.5 - 0 = 0.5
here we see -0.5 ≠ 0.5
but f(-0.5) = f(0.5)
hence, f(x) is many one function.
so, inverse of f(x) doesn't exist.
option (a) is correct.
f(x) = x - [x] also written as {x} ,range of fractional part of x is 0 ≤ x < 1.
if we take two different values of x
e.g., -0.5 and 0.5
then, f(-0.5) = -0.5 - [-0.5] = -0.5 -(-1) = 0.5
f(0.5) = 0.5 - [0.5 ] = 0.5 - 0 = 0.5
here we see -0.5 ≠ 0.5
but f(-0.5) = f(0.5)
hence, f(x) is many one function.
so, inverse of f(x) doesn't exist.
option (a) is correct.
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