which equation is the inverse of $y = 100 - x^2$?\n$\\bigcirc$ $y = \\pm \\sqrt{100 - x}$\n$\\bigcirc$ $y =…

which equation is the inverse of $y = 100 - x^2$?\n$\\bigcirc$ $y = \\pm \\sqrt{100 - x}$\n$\\bigcirc$ $y = 10 \\pm \\sqrt{x}$\n$\\bigcirc$ $y = 100 \\pm \\sqrt{x}$\n$\\bigcirc$ $y = \\pm \\sqrt{x - 100}$

which equation is the inverse of $y = 100 - x^2$?\n$\\bigcirc$ $y = \\pm \\sqrt{100 - x}$\n$\\bigcirc$ $y = 10 \\pm \\sqrt{x}$\n$\\bigcirc$ $y = 100 \\pm \\sqrt{x}$\n$\\bigcirc$ $y = \\pm \\sqrt{x - 100}$

Answer

Explanation:

Step1: Swap x and y

To find the inverse of a function, we first swap the roles of ( x ) and ( y ) in the equation ( y = 100 - x^2 ). So we get ( x = 100 - y^2 ).

Step2: Solve for y

Now, we solve the new equation for ( y ). First, we rearrange the equation to isolate ( y^2 ). Subtract ( x ) from both sides and add ( y^2 ) to both sides: ( y^2 = 100 - x ). Then, take the square root of both sides. Remember that when we take the square root, we have to consider both the positive and negative roots, so ( y=\pm\sqrt{100 - x} ).

Answer:

( y=\pm\sqrt{100 - x} ) (the first option)