Domain = (-∞,∞) and Range = [-2,∞) of the given function [tex]f(x) = 3|x + 7| - 2[/tex].
What is domain of the function?
" Domain is defined as all the input values of the given independent variable of the given function."
What is range of the function?
" Range is defined as all the output values of the given dependent variable of the given function."
According to the question,
Given function,
[tex]f(x) = 3|x + 7| - 2[/tex]
'x' increases f(x)→∞
'x' decreases f(x)→ (-∞)
Therefore,
Domain of the function is set of all real value ( -∞ , ∞).
For the given function [tex]f(x)[/tex],
[tex]|x +7 | \geq 0[/tex]
⇒ [tex]3|x +7 | \geq 0[/tex]
⇒[tex]3|x +7 |-2\geq 0-2[/tex]
⇒[tex]3|x +7 |-2\geq -2[/tex]
Therefore,
Range of f(x) = [-2 , ∞)
Hence, domain = (-∞,∞) and range = [-2,∞) of the given function [tex]f(x) = 3|x + 7| - 2[/tex].
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