Answer:
The inverse of g(x) should be [tex]\sqrt{(x-3)}[/tex].
Step-by-step explanation:
The inverse means the opposite. The opposite of a term or expression squared will be the terms or expression square rooted.
The inverse of (x-3)² will be [tex]\sqrt{x-3}[/tex]
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Answer:
g(x)⁻¹ = √x + 3
Step-by-step explanation:
To find the inverse of an expression is to reverse the expression. This can be done by swapping the input and output variables. In other words, in g(x), you want to swap the places of the "x" variable the "y" variable.
Remember, g(x) = y.
y = (x - 3)² <----- Original function
x = (y - 3)² <----- Swap the variables
Now, you want to set the equation equal to "y" again. This can be done by rearranging/simplifying the expression.
x = (y - 3)² <----- Swapped variables
√x = √(y - 3)² <----- Take the square root of both sides
√x = y - 3 <----- Eliminate parentheses from previous step
√x + 3 = y <----- Add 3 to both sides
If g(x)⁻¹ represents the inverse of g(x), the new function is:
g(x)⁻¹ = √x + 3
