- #1
applestrudle
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Homework Statement
f(x)= 2x + x^2
Homework Equations
The Attempt at a Solution
I don't know how to make x the subject
applestrudle said:Homework Statement
f(x)= 2x + x^2
Homework Equations
The Attempt at a Solution
I don't know how to make x the subject
Ray Vickson said:You need to solve for x in the equation x^2 + 2x = y. This is a simple quadratic equation.
No.applestrudle said:Okay thank you!
I've got it:
X^2 +2x = y
add one so you get a quadratic that has a "squared"
x^2 +2x +1 = y + 1
solve quadratic:
(x+1)^2 = y + 1
x = (y+1)^-1/2 -1
Note that the equation y = x2 + 2x does not give y as a 1-to-1 function of x, so there is no inverse function, unless you place restrictions on the domain.applestrudle said:f-1(x) = (x+1)^-1/2 -1
:)
You have raised to the power -1/2. Where did the negative sign come from?applestrudle said:f-1(x) = (x+1)^-1/2 -1
:)
oay said:You have raised to the power -1/2. Where did the negative sign come from?
To find the inverse function of a function with an x^2+x term, you can use the following steps:
No, you cannot use the quadratic formula to find the inverse function of x^2+x. The quadratic formula is used to solve for x in a quadratic equation, not to find inverse functions. You can use the steps outlined in question 1 to find the inverse function of x^2+x.
Yes, the inverse function of x^2+x is always a one-to-one function. This is because the original function has a unique output for every input, and the inverse function simply switches the input and output values. Therefore, it also has a unique output for every input, making it a one-to-one function.
To graph the inverse function of x^2+x, you can use the following steps:
While some calculators have the ability to find inverse functions, they may not work for all functions, including x^2+x. It is best to use the steps outlined in question 1 to find the inverse function of x^2+x manually.