SOLUTION: Determine the equation of the inverse for the quadratic equation
f(x)=6x^2+11
I don’t know how to do this one since my teacher didn’t explain this one
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f(x)=6x^2+11
I don’t know how to do this one since my teacher didn’t explain this one
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Question 1197339: Determine the equation of the inverse for the quadratic equation
f(x)=6x^2+11
I don’t know how to do this one since my teacher didn’t explain this one Found 2 solutions by math_tutor2020, MathLover1:Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Graph out y = 6x^2+11 to find that it fails the horizontal line test.
It is possible to draw a single horizontal line through more than one point on the parabola.
This function is not one-to-one, i.e. the function is not injective.
As such, no inverse exists if we account for the entire domain of f(x) = 6x^2+11
But if we restrict the domain to , then the graph passes the horizontal line test. This is the right hand side of the parabola.
The outline to finding the inverse follows these steps
1) Replace f(x) with y
2) Swap x and y
3) Solve for y
Let's follow that process
f(x) = 6x^2+11
y = 6x^2+11
x = 6y^2+11
x-11 = 6y^2
6y^2 = x-11
y^2 = (x-11)/6
y = sqrt( (x-11)/6 )
The inverse is
The green graph represents the original function f(x) = 6x^2+11 but only when
The inverse is the blue curve, which is a reflection of the green curve over the dashed purple line y = x
You can put this solution on YOUR website!
to determine the equation of the inverse for the quadratic equation, recall that ...... swap variables
..........solve for
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