Answer:
The inverse of the equation is [tex]f^{-1}(x)=\pm\sqrt{\frac{x-1}{16}}[/tex]
Step-by-step explanation:
Given : Equation [tex]y=16x^2+1[/tex]
To find : The inverse of the equation ?
Solution :
Equation [tex]y=16x^2+1[/tex]
To find the inverse we interchange the value of x and y,
[tex]x=16y^2+1[/tex]
Now, solve for y
[tex]16y^2=x-1[/tex]
Divide by 16 both side,
[tex]y^2=\frac{x-1}{16}[/tex]
Taking root both side,
[tex]y=\pm\sqrt{\frac{x-1}{16}}[/tex]
[tex]f^{-1}(x)=\pm\sqrt{\frac{x-1}{16}}[/tex]
Therefore, The inverse of the equation is [tex]f^{-1}(x)=\pm\sqrt{\frac{x-1}{16}}[/tex]
