# How I found the value

I would like to know how to find the value of a function.

For example, consider one the most basic funcions

y[x] = x^2


The ploy is a parabola. So if I want y = 1200, I need to see on the graph approximate values to test for x to find it.

My questions is, in mathematica is there a function or any command where I can write y = 1200 and automatically generate the value of x?

• Try Solve like Solve[1200 == x^2, x] Commented Sep 3, 2020 at 22:25

The first option is always Solve (also NSolve). As @Jason showed, using Solve with a specific value will give you all possible solutions

f[x_] = x^2
Solve[f[x] == 1.2, x]


{{x -> -1.09545}, {x -> 1.09545}}

On the other hand as @Mark showed,

Solve[y == f[x], x]


{{x -> -Sqrt[y]}, {x -> Sqrt[y]}}

will give you all possible analytical solutions which you can use to generate values of x for any y. However these methods can be tricky when you have large and complicated functions (specially trigonometric functions where you might have to specify the domain like 0<x<2Pi as well). In that case you can use FindRoot

FindRoot[f[x] == 1.2, {x, 1.0}]
FindRoot[f[x] == 1.2, {x, -1.0}]


{x -> 1.09545} {x -> -1.09545}

FindRoot` requires an initial guess and gives only one numerical solution closest to the initial guess.

• Thanks for help me Commented Sep 7, 2020 at 22:48