Question - Finding the Inverse of a Function
Solution:
To find the inverse of the function $$ f(x) = \sqrt{x} - 2 $$, we need to switch the roles of x and y and then solve for y. Here are the steps:1. Write the original function with y: $$ y = \sqrt{x} - 2 $$.2. Swap x and y: $$ x = \sqrt{y} - 2 $$.3. Solve for y: Starting with the equation from step 2, we will isolate y:\[ x = \sqrt{y} - 2 \]\[ x + 2 = \sqrt{y} \] (Add 2 to both sides)Now we need to get rid of the square root by squaring both sides of the equation:\[ (x + 2)^2 = y \]So the inverse function $$ f^{-1}(x) $$ is:\[ f^{-1}(x) = (x + 2)^2 \]
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