Question

g(x) = x + 4 and h(x) = x^2 - 3

g[h(x)] = _____.

A.x + 1
B.x 2 + 3
C.x 2 + 1
D.x 2 + 8x + 19

Answer 1

you have to combine the two functions

Answer 2

If you were to be asked to find \(\large\color{slate}{ g(\color{red}{D}) }\)

having the function: \(\large\color{slate}{ g(x) = x + 4 }\)

you would do this:
\(\large\color{slate}{ g(\color{red}{D}) =(\color{red}{D}) + 4 }\)

Now, however, they are asking for \(\large\color{slate}{ g[\color{red}{h(x)}] }\)
which just means that you are plugging the h(x) into the g(x) for x.

knowing that \(\large\color{slate}{ h(x) = x^2 - 3 }\) (which they explicitly tell you)

So lets plug in h(x) for x, into the function g(x).
\(\large\color{slate}{ g[\color{red}{h(x)}] = (\color{red}{x^2 - 3}) + 4 }\)

Answer 3

See what you are asked to do?
Can you simplify this?

Answer 4

x^2+1?

Answer 5

yes, that is correct
\(\large\color{slate}{ g[\color{red}{h(x)}] = x^2+1 }\)

Answer 6

okay I get this now thank you

Answer 7

Sure:) ... you welcome !