exercise:D8cd0664e8

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Let [math]f(x)[/math] be a given function and [math]L[/math] a linear operator. Define [math]f(x)L[/math] by the equation

[[math]] (f(x)L)y =f(x)(L_y) . [[/math]]

Show that [math]f(x)L[/math] satisfies equation and equation and hence is a linear operator.