we have
[tex]y=16x^{2} +1[/tex]
Step 1
Exchange the variables x for y and y for x
[tex]x=16y^{2} +1[/tex]
Step 2
Clear variable y
[tex]x=16y^{2} +1[/tex]
Subtract [tex]1[/tex] both sides
[tex]x-1=16y^{2} +1-1[/tex]
[tex]x-1=16y^{2}[/tex]
Divide by [tex]16[/tex] both sides
[tex](x-1)/16=16y^{2}/16[/tex]
[tex](x-1)/16=y^{2}[/tex]
square root both sides
[tex]y=(+/-)\sqrt{\frac{x-1}{16}} \\ \\y=(+/-) \frac{1}{4} \sqrt{x-1}[/tex]
Step 3
Find the inverse
Let
[tex]f(x)^{-1} =y[/tex]
so
[tex]f(x)^{-1}=(+/-) \frac{1}{4} \sqrt{x-1}[/tex]
therefore
the answer is
[tex]f(x)^{-1}=(+/-) \frac{1}{4} \sqrt{x-1}[/tex]
