Answer:
[tex]y=\frac{\sqrt{x-1} }{4}[/tex]
Step-by-step explanation:
The given equation is
[tex]y=16x^2+1[/tex]
For this function to have an inverse, we must restrict the domain, say [tex]x\ge0[/tex]
We interchange x and y to get,
[tex]x=16y^2+1[/tex]
We now make y the subject to get;
[tex]x-1=16y^2[/tex]
[tex]x-1=16y^2[/tex]
We divide through by 16 to get;
[tex]\frac{x-1}{16}=y^2[/tex]
We now take the square root of both sides to get;
[tex]\pm \sqrt{\frac{x-1}{16}}=y[/tex]
[tex]y=\pm \frac{\sqrt{x-1} }{4}[/tex]
Since [tex]x\ge 0[/tex], the inverse function is
[tex]y=\frac{\sqrt{x-1} }{4}[/tex]
