Question

Which equation is the inverse of y = 16x2 + 1?

Answer 1

we have

$y=16x^{2} +1$

Step 1

exchange variables x for y and y for x

$x=16y^{2} +1$

Step 2

Isolate the variable y

Subtract $1$ both sides

$x-1=16y^{2}+1-1$

$16y^{2}=x-1$

Divide by $16$ both sides

$16y^{2}/16=(x-1)/16$

$y^{2}=\frac{x-1}{16}$

Square root both sides

$y=(+/-)\sqrt{\frac{x-1}{16}}$

$y=(+/-)\frac{\sqrt{x-1}}{4}$

Step 3

Let

$f(x)^{-1}=y$

$f(x)^{-1}=(+/-)\frac{\sqrt{x-1}}{4}$

therefore

the answer is

The inverse is equal to

$f(x)^{-1}=(+/-)\frac{\sqrt{x-1}}{4}$

Answer 2

The inverse of the function is y = \sqrt{x+1/16}

Inverse of functions

Given the expression

y = 16x² + 1

We see to find the inverse of the function

Replace y with x to have;

x = 16y² - 1

Make y the subject of the formula

16y² = x + 1

Divide both sides by 16

16y²/16 = x+1/16

y² = x+1/16

Take the square root of both sides

y = \sqrt{x+1/16}

Hence the inverse of the function is y = \sqrt{x+1/16}

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