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Answer: [tex]\pm 3[/tex]
Step-by-step explanation:
Just to clarify, we cannot solve [tex]g(x) = 2x^2 + 3[/tex]. This is a function.
A function is like a machine that takes in a value (called the input) and returns another value (called the output). Here, x is the input, and g(x) is the output. By putting in a number for x, we get a different number, which is also known as g(x).
We want to find x when g(x) = 21. Since g(x) is a variable, we can replace it in the original equation.
[tex]21 = 2x^2 + 3[/tex]
Now, we need to do some algebra to solve for x. We do this by isolating the variable, or undoing everything being done on the variable to find its value. Basically, we are looking for the x that was put in the function in the first place to get g(x).
We first should subtract 3. This will remove the addition of 3 at the end:
[tex]21 - 3 = 2x^2 + 3 - 3\\18 = 2x^2[/tex]
Next, divide both sides by 2. This will get rid of the 2 in front of the x:
[tex]\frac{18}{2} = \frac{2x^2}{2}\\ 9 = x^2[/tex]
Finally, we need to take the square root of both sides.
[tex]\sqrt(9) = \sqrt(x^2)\\3 = x[/tex]
But we are not done yet. For the previous statement, -3 would have also worked, since (-3)^2 = 9 too. That's why we indicate that [tex]x = \pm 3[/tex], meaning positive or negative 3 would work for the answer.