The range of the function f(x) is [-1/2, 1/2].
What is the range of a function?
The range is the set of possible output values, which are shown on the y-axis. The range of a function, f is the set of all values f(x) , such that x is in the domain of f. Graphically speaking, the range is the set of all y such that (x,y) is a point on the graph of f.
For the given situation,
The function f(x) = 1/2sin(2x-π)
The graph below shows the range of the function f(x) = 1/2sin(2x-π) graphically.
As the range of sinx function is [-1, 1], the range of sin2x is also [-1, 1].
Let us consider [tex]\theta = 2x-\pi[/tex]
⇒ Then, [tex]sin \theta[/tex] lies in the range [tex][-1,1][/tex]
⇒ [tex]-1\leq sin(2x-\pi )\leq 1[/tex]
⇒ [tex](\frac{1}{2} )(-1)\leq sin(2x-\pi )\leq( 1)(\frac{1}{2} )[/tex]
⇒ [tex]\frac{-1}{2} \leq sin(2x-\pi )\leq\frac{1}{2}[/tex]
Hence we can conclude that the range of the function f(x) is [-1/2, 1/2].
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