Answer:
14)
![x=3](https://img.qammunity.org/2021/formulas/mathematics/college/yzekanmiuar9edsve93wg5dpqbw3650n5b.png)
16)
![(g\circ f)(2)=1](https://img.qammunity.org/2021/formulas/mathematics/high-school/j93luqugifwdp7ox8706owfrab6vc6a0xe.png)
Explanation:
We have the two functions:
and
.
14)
We want to find x if
.
In other words, we want to find for what value of x does f(x) equal 3.
So, to do so, we can substitute our equation,
, for f(x) and solve for x. This gives us:
![2x-3=3](https://img.qammunity.org/2021/formulas/mathematics/high-school/fn2fs64rdy8ccfzyff0q0jdhl6prx45hkq.png)
Solve for x. Add 3 to both sides:
![2x=6](https://img.qammunity.org/2021/formulas/mathematics/middle-school/6sesyg6t9z5pu68t33pbgi41i56b0t8uwz.png)
Divide by 2:
![x=3](https://img.qammunity.org/2021/formulas/mathematics/college/yzekanmiuar9edsve93wg5dpqbw3650n5b.png)
So,
, and our x is 3.
16)
We have:
![(g\circ f)(2)](https://img.qammunity.org/2021/formulas/mathematics/high-school/h3fwg1e5a9rrzb4ux55krn3m7zwhn3whbf.png)
This is known as composition of functions. This is equivalent to
![g(f(2))](https://img.qammunity.org/2021/formulas/mathematics/high-school/nss3iw8pxvcmhc0lhkli3m3ypfbe8k7knz.png)
So, let's find f(2) first. We know that:
![f(x)=2x-3](https://img.qammunity.org/2021/formulas/mathematics/high-school/hn9xamord6ey4x9vwq1sewj3nb8lukmej0.png)
Substitute 2 for x:
![f(2)=2(2)-3](https://img.qammunity.org/2021/formulas/mathematics/high-school/7ol18trqr06i8w3vhyflpdkj8k5utba50q.png)
Evaluate:
![f(2)=4-3=1](https://img.qammunity.org/2021/formulas/mathematics/high-school/m6hvvomyrl6525twfyqanl4xl6hc0go6zc.png)
Therefore, our composition of functions can be rewritten as:
![g(f(2))=g(1)](https://img.qammunity.org/2021/formulas/mathematics/high-school/wrd5yka2ul3sroxuk5etvbb5vi729utget.png)
Find g(1). We know that:
![g(x)=x^2](https://img.qammunity.org/2021/formulas/mathematics/middle-school/gdz7ck11howgid8wvht6l4801jaqidgqyu.png)
Substitute 1 for x:
![g(1)=(1)^2](https://img.qammunity.org/2021/formulas/mathematics/high-school/y9e6d01886ovps9pno0tr6cuv0glotpwej.png)
Evaluate:
![g(1)=1](https://img.qammunity.org/2021/formulas/mathematics/high-school/tw7jozmrakvzpk5gmne1nhdqd7sblvpbpw.png)
Therefore:
![(g\circ f)(2)=1](https://img.qammunity.org/2021/formulas/mathematics/high-school/j93luqugifwdp7ox8706owfrab6vc6a0xe.png)