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The domain of a function is the set of input values the function can take, while the range is the set of output values of the function
The true statements are: statements (a) and (c)
(a) Range and the domain of [tex]f(x) = \sqrt x[/tex] and [tex]f(x) = 2\sqrt {x[/tex].
Both functions are square root functions, and they have the same range and domain
Hence, statement (a) is true
(b) Range and the domain of [tex]f(x) = \sqrt x[/tex] and [tex]f(x) =-2 \sqrt {x[/tex].
Both functions are square root functions, with the same domain.
However, [tex]f(x) = -2\sqrt x[/tex] has a negative range
Hence, statement (b) is false
(c) Range and the domain of [tex]f(x) = \sqrt x[/tex] and [tex]f(x) = -\sqrt {x[/tex].
Both functions are square root functions, and they have the same domain but different range
This is so because
[tex]f(x) = -\sqrt x[/tex] has a negative range
Hence, statement (a) is true
(d) Range and the domain of [tex]f(x) = \sqrt x[/tex] and [tex]f(x) =\frac 12 \sqrt {x[/tex].
Both functions are square root functions, with the same domain and range.
Hence, statement (d) is false
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