Given d(x)=16x^2 - 5 find d^-1(x)
To find the inverse of a function, we need to switch the roles of x and y and then solve for y.
Let us switch the roles of x and y in the equation d(x) = 16x^2 - 5:
x = 16y^2 - 5
Now, let's solve for y. Rearranging the equation, we have:
16y^2 = x + 5
Dividing both sides by 16:
y^2 = (x + 5)/16
Taking the square root of both sides:
y = ±√((x + 5)/16)
Here, y can take both positive and negative values. Hence, the inverse function is:
d^-1(x) = ±√((x + 5)/16)