The functions are inverse function because (d) [tex]\sqrt{g(x) -5} + 4[/tex]
How to determine the inverse statement?
The functions are given as:
[tex]f(x) = \sqrt{x -5} + 4[/tex]
[tex]g(x) = (x - 4)^2 + 5[/tex]
If the functions are inverse functions, then
f(g(x)) = x
Start by calculating f(g(x)), as follows:
[tex]f(x) = \sqrt{x -5} + 4[/tex]
[tex]f(g(x)) = \sqrt{g(x) -5} + 4[/tex]
This gives
[tex]f(g(x)) = \sqrt{(x - 4)^2 + 5 -5} + 4[/tex]
Evaluate the difference
[tex]f(g(x)) = \sqrt{(x - 4)^2} + 4[/tex]
Evaluate the exponent
f(g(x)) = x - 4 + 4
Evaluate the difference
f(g(x)) = x
Hence, the functions are inverse function because [tex]\sqrt{g(x) -5} + 4[/tex]
Read more about inverse functions at:
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