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