If g(x)=5-3x^2 find g(-2) find g(a+2)

Mathematics
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If g(x)=5-3x^2 find g(-2) find g(a+2) How do I solve this

Aug 25th, 2015

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

Please let me know if you need any clarification. Always glad to help!
Aug 25th, 2015

Thank you so much for the help, how does the foil work you just multiply out? and also what would the end answer be. Thank you


Aug 25th, 2015

whenever you have an expression like (a+2)^2 what is actually going on is that you are multiplying (a+2) times itself:

(a+2)*(a+2)

FOIL just means that we multiply out the First terms, then the Outer terms, then the Inner terms, and finally the Last terms. In this case

First: a*a

Outer: a*2

Inner: 2*a

Last: 2*2 = 4

Adding them all up gives a^2 + 2a+2a+4 = a^2+4a+4.

The final answer is -3a^2-12*a-7, in bold in the previous answer

Aug 25th, 2015

Okay great, so for the one with g(-2) would be 2=5-7? as the answer thanks again

Aug 25th, 2015

g(-2) = 5 - 3* (-2)^2 = 5 - 3*(4) = 5 - 12 = -7.

The final answer is 5 -12 which is  -7 

Aug 25th, 2015

Okay so what happens with the 2= that was at the beginning

Aug 25th, 2015

I don't see what you are pointing to...There is one expression:

g(-2) = 5 -3*(-2)^2

This simplifies to

g(-2) = 5-3*(4)

[because (-2)^2 = 4]

Then we multiply -3*4 giving us:

g(-2) = 5-12

And we perform the last subtraction

g(-2)= -7

Aug 25th, 2015

sorry for all fo the questions but if we were to look at one more that is d(x)=2x+1 find D(2) would the result be d(2)=5

Aug 25th, 2015

Yes, exactly! 

Aug 25th, 2015

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