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What is the inverse of f(x) = (x - 5)^2 for x ≥ 5 where function g is the inverse of function f?A) g(x) = ✓x - 5, x ≥ 0B) g(x) = ✓x - 5, x ≥ 5C) g(x) = ✓x + 5, x ≥ 0D) g(x) = ✓x + 5, x ≥ -5

What is the inverse of fx x 52 for x 5 where function g is the inverse of function fA gx x 5 x 0B gx x 5 x 5C gx x 5 x 0D gx x 5 x 5 class=

Respuesta :

The given function is

[tex]f(x)=(x-5)^2,x\ge5[/tex]

To find its inverse g(x) we will do these steps

1. Replace f(x) by y

[tex]y=(x-5)^2[/tex]

2. Switch x and y

[tex]x=(y-5)^2[/tex]

3. Solve to find y

Take a square root for both sides

[tex]\begin{gathered} \sqrt[]{x}=\sqrt[]{(y-5)^2} \\ \sqrt[]{x}=y-5 \end{gathered}[/tex]

Add 5 to both sides

[tex]\begin{gathered} \sqrt[]{x}+5=y-5+5 \\ \sqrt[]{x}+5=y \end{gathered}[/tex]

4. Replace y by g(x)

[tex]g(x)=\sqrt[]{x}+5,x\ge0[/tex]

The answer is the 3rd choice

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