Question

The function g is such that g(x)=2x²-20x+9 where x>=5

Express the inverse function g⁻¹ in the form g⁻¹(x)

Answer 1

The inverse function g⁻¹(x) of g(x) = 2x² - 20x + 9 is g⁻¹(x) = 5 ± √(7 + 2x).

Step-by-step explanation:

To find the inverse function, g-1(x), of g(x) = 2x² - 20x + 9, we need to swap the x and y variables and solve for y. So, we have:

x = 2y² - 20y + 9

Let's rearrange the equation to isolate y:

2y² - 20y + 9 - x = 0

We can use the quadratic formula to solve for y:

y = (20 ± √(20² - 4(2)(9-x)))/(2(2))

Now, simplify the expression:

y = (10 ± √(100 - 8(9-x)))/2

y = (10 ± √(100 - 72 + 8x))/2

y = (10 ± √(28 + 8x))/2

y = 5 ± √(7 + 2x)

The inverse function g-1(x) = 5 ± √(7 + 2x)