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