Find the inverse of F. Then sketch the graphs of f and f ^-¹ on the same set of axes.f (x) = , x $\ge$ 0 A)f ^-¹(x) = - , x $\ge$ 0 B)f ^-¹(x) = , x $\ge$ 0 C)f ^-¹(x) = , x $\ge$ 0 D)f ^-¹(x) = - , x $\ge$ 0

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Quizplus · Accepted Answer

To find the inverse of f, we need to solve for x in terms of y. y = 11e^(x^2-5x-6) Taking the natural logarithm of both sides: ln(y) = (x^2-5x-6)ln(11) Solving for x using the quadratic formula: x = (5 +/- sqrt(25+4ln(y)ln(11))) / 2 Therefore, the inverse function is: f^-1(x) = (5 +/- sqrt(25+4ln(x)ln(11))) / 2 Now, to sketch the graph of f ^-¹ on the same set of axes as f, we can use the transformation rules: - f ¹ reflects f over the y-axis - f ^{shifts f left by 1 unit
- f} shifts the reflected function back over the y-axis - f ^{1 shifts the function up by 1 unit.
Overall, this transformation results in a new function with the same shape as f, but shifted to the left and up by one unit and reflected over the y-axis. Using these rules, we can see that the correct choice is B.}

Find the Inverse of F ≥\ge≥ 0 A)f -1(x) = - , X

Find the Inverse of F $\ge$ 0

A)f ^-¹(x) = - , X