The absolute value of a number |x|, is defined as `|x| = x, x>= 0` and `|x| = -x, x < 0` .
The function `G(x) = (3x+|x|)/x` can be rewritten for different values of x as:
`G(x) = (3x + x)/x, x > 0`
= `(4x)/x, x > 0`
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The absolute value of a number |x|, is defined as `|x| = x, x>= 0` and `|x| = -x, x < 0` .
The function `G(x) = (3x+|x|)/x` can be rewritten for different values of x as:
`G(x) = (3x + x)/x, x > 0`
= `(4x)/x, x > 0`
= `4, x > 0`
When x = 0, `G(x) = (3x + x)/x = 0/0` which is indeterminate.
`G(x) = (3x - x)/x, x < 0`
= `(2x)/x, x < 0`
= `2, x <0`
The value of G(x) is real and defined for all values of x except 0.
The domain of the function is R - {0}
The graph of this function is: