Determine Whether the Function Has an Inverse Function $$f ( x ) = x ^ { 2 } + 5$$

question 81

Multiple Choice

Determine whether the function has an inverse function.If it does, find the inverse function. $$f ( x ) = x ^ { 2 } + 5$$

• A) No inverse function exists.
• B) \(f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0\)
• C) \(f ^ { - 1 } ( x ) = \sqrt { x } - 5\)
• D) \(f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 6\)
• E) \(f ^ { - 1 } ( x ) = \sqrt { x - 5 }\)

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Definitions:

Sum of Squares for Error

The sum of the squared differences between the observed value and the estimated value of the parameter of interest, used as a measure of variation within a dataset.

Sum of Squares for Regression

The sum of squares for regression quantifies the variation explained by the regression model, comparing the fitted values against the mean of the dependent variable.

SSR

Stands for Sum of Squares due to Regression, which measures the variation explained by the regression line in the context of statistical analysis.

Simple Linear Regression

A statistical method for examining the linear relationship between two quantitative variables; one variable is used to predict the outcome of another.