Answer:
[tex]g(x)=\sqrt{x}-6[/tex], x>=0
Step-by-step explanation:
[tex]f(x)=(x+6)^2[/tex]
To find the inverse function , replace f(x) by y
[tex]y=(x+6)^2[/tex]
Replace x with y and y with x
[tex]x=(y+6)^2[/tex]
Solve the equation for y
take square root on both sides
[tex]+\sqrt{x} =y+6[/tex]
Now subtract 6 from both sides
[tex]+\sqrt{x}-6=y[/tex]
replace y with g(x)
[tex]g(x)=\sqrt{x}-6[/tex]
The inverse of a function is its opposite
The inverse of the function is [tex]\mathbf{g(x) = \sqrt x - 6}[/tex] x >= 0
The function is given as:
[tex]\mathbf{f(x) = (x + 6)^2}[/tex]
Rewrite as:
[tex]\mathbf{y = (x + 6)^2}[/tex]
Swap x and y
[tex]\mathbf{x = (y + 6)^2}[/tex]
Take square roots of both sides
[tex]\mathbf{\sqrt x = y + 6}[/tex]
Subtract 6 from both sides
[tex]\mathbf{y = \sqrt x - 6}[/tex]
Rewrite as:
[tex]\mathbf{g(x) = \sqrt x - 6}[/tex]
Hence, the inverse of the function is [tex]\mathbf{g(x) = \sqrt x - 6}[/tex] x >= 0
Read more about inverse functions at:
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