Step by step
The question
Question: find x when f(x) = 3 for f(x) = x² + 4.
f(x) = x2 + 4
f(x) = 3 means: the answer that comes out is 3.
We look for the x that goes in.
f(x) = 3: 3 comes out
find what goes in
Careful!
It is not f(3).
3 is what comes out, not what goes in.
Careful: not f(3) ✗
1 Write the equation
f(x) is x² + 4.
So x² + 4 = 3.
Now we solve it.
x2 + 4 = 3
2 Get x² alone
There is no x term, so we get x² by itself.
To remove the + 4, we take away 4 on both sides.
x2 + 4 − 4 = 3 − 4
3 − 4 = −1.
Now we have x² = −1.
x2 = −1
3 Square root of both sides
x squared is −1.
But a real number times itself is never negative.
So there is no real solution.
x2 = −1 no real solution
Let's look back.
First: write the equation.
Then: get x² alone.
Last: square root of both sides.
Answer
x2 = −1 no real solution