Description
If g(x)=5-3x^2 find g(-2) find g(a+2) How do I solve this
Explanation & Answer
Hi there! Thank you for the opportunity to help you with your question!
When we have a function g(x) = 5 - 3*x^2, what we are actually saying is that wherever you see the value "x", you should replace by the value inside the parenthesis. That is if I asked you what was g(y), it would be 5-3y^2, if I asked for g(397) = 5-3(397)^2.
In your problem, they ask for g(-2), which means we have to plug in (-2) wherever you see an x.
g(-2) = 5 - 3* (-2)^2 = 5 - 3*(4) = 5 - 12 = -7.
Now for the second part, we need to plug in (a+2) wherever we see an x:
g(a+2) = 5 - 3*(a+2)^2
We could simplify the expression a little bit more, by using FOIL to multiply out the squared term:
g(a+2) = 5 - 3*(a+2)^2 = 5 - 3*(a^2 + 4*a + 4) = 5 - 3*a^2 -12*a -12 = -3a^2-12*a-7
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