Answer:
The range is the resulting y-values we get after substituting all the possible x-values.
For the given function : [tex]f(x) = \frac{3}{4x} -4[/tex]
See the attached figure.
The zeros of the denominator at x = 0
The domain is: (-∞,0)∪(0,∞)
The range of the function is the domain of the inverse function of f(x)
y = 3/(4x) - 4
y + 4 = 3/(4x)
4x = 3/(y+4)
[tex]x=\frac{3}{4(y+4)}[/tex]
The zeros of the inverse function:
4(y+4) = 0
y + 4 = 0
y = -4
∴ The range is (-∞,-4)∪(-4,∞)
So, the answer is {y | y > –4} ∪ {y | y < – 4}
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Note: If the given function is : [tex]f(x) = \frac{3}{4} x-4[/tex]
It will be first degree polynomial function.
Both of the domain and the range = all real numbers R
