Question

1. determine the inverse of the function by interchanging the variables and solving for ( y ) in terms of ( x ).( y = 4x^2 )options: ( y=pmsqrt{x} ); ( y = pm2x ); ( y=\frac{pmsqrt{x}}{2} ); ( y=pm4sqrt{x} )7) determine the inverse of the function by interchanging the variables and solving for ( y ) in terms of ( x ).( y = x^2 - 1 )options: ( y = 1pmsqrt{x} ); ( y=-1pmsqrt{x} ); ( y=pmsqrt{x + 1} ); ( y=-x^2 + 1 )8) apply the horizontal or vertical line test to determine if the inverse of the function will be a function.is the inverse of the function a function? image of a graphoptions: no; yes

Explanation:

Step1: Swap $x$ and $y$ for Q6

$x=4y^2$

Step2: Isolate $y^2$ for Q6

$y^2=\frac{x}{4}$

Step3: Solve for $y$ for Q6

$y=\pm\sqrt{\frac{x}{4}}=\pm\frac{\sqrt{x}}{2}$

Step4: Swap $x$ and $y$ for Q7

$x=y^2-1$

Step5: Isolate $y^2$ for Q7

$y^2=x+1$

Step6: Solve for $y$ for Q7

$y=\pm\sqrt{x+1}$

Step7: Horizontal line test for Q8

The original graph fails the horizontal line test (a horizontal line intersects it at 2 points), so its inverse fails the vertical line test, meaning it is not a function.

Answer:

1. $\boldsymbol{y=\pm\frac{\sqrt{x}}{2}}$
2. $\boldsymbol{y=\pm\sqrt{x+1}}$
3. $\boldsymbol{No}$