What is the solution for f(t,t^2)?

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In summary, "Solving for f(t,t^2): "2t" means finding the function f(t,t^2) where t squared is equal to 2t. To solve for f(t,t^2) when given the equation "2t", we can rewrite it as 2t = t^2 and use algebraic manipulation to find a possible solution, such as f(t,t^2) = t. However, there can be multiple solutions for f(t,t^2) for a given equation. There may also be restrictions on the values of t, such as t ≠ 0 in this case. The solution for f(t,t^2) can be graphically represented by plotting points on a graph,
  • #1
brendan
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Homework Statement



Let f(x,y) = x + (xy)^1/3

Find f(t,t^2)

Homework Equations





The Attempt at a Solution



Do I just substitute the t values into the original equation?

f(x,y) = x + (xy)^1/3

f(x,y) = t+ (tt^2)^1/3

f(x,y) = t + t

f(x,y) = 2t
 
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  • #2
Looks good to me.
 
  • #3
Thanks
Brendan
 

1. What is the meaning of "Solving for f(t,t^2): "2t"?

"Solving for f(t,t^2): "2t" means finding the function f(t,t^2) that when t is squared, it equals 2t."

2. How do you solve for f(t,t^2) when given the equation "2t"?

To solve for f(t,t^2), we can first rewrite the given equation as 2t = t^2. Then, we can use algebraic manipulation to solve for t and f(t,t^2). One possible solution is f(t,t^2) = t.

3. Can there be more than one solution for f(t,t^2) when given the equation "2t"?

Yes, there can be multiple solutions for f(t,t^2) when given the equation "2t". For example, f(t,t^2) = t and f(t,t^2) = -t^2 are both valid solutions to the equation 2t = t^2.

4. Are there any restrictions on the values of t when solving for f(t,t^2) in the equation "2t"?

Yes, there may be restrictions on the values of t depending on the given equation. In this case, since t^2 cannot equal 0 (as it would result in a division by 0), the restriction for t would be t ≠ 0.

5. How can the solution for f(t,t^2) be graphically represented when given the equation "2t"?

The solution for f(t,t^2) can be graphically represented by plotting the points (t, f(t,t^2)) on a graph. In this case, the points would form a straight line with slope 2 and x-intercept 0.

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