Question

PLEASE HELP

Answer 1

Our function. y=(x^2 ) +6
The inverse function switches from (x,y) to (y, x) so where you see y put a x and where you see x put a y.
Inverse function. X=(y^2)+6
Now we still needed to have it in the form of y= something so lets work it.
X-6=y^2
Square root (x-6)=y
f^-1 (x)=square root (x-6)

Answer 2

f(x)=x^2−6

Replace f(x) with yy.

y=x^2−6

Interchange the variables.

x=y2−6

Solve for yy.

Move −6-6 to the right side of the equation by subtracting −6-6 from both sides of the equation.y2=6+xy2=6+xTake the squaresquare root of both sides of the equationequation to eliminate the exponent on the left side.y=±√6+xy=±6+x

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

y=√6+x,−√6+x
Solve for y and replace with f^−1(x).

Answer is f−1(x)=√6+x,−√6+x