Answer:
14) [tex]x=3[/tex]
16) [tex](g\circ f)(2)=1[/tex]
Step-by-step explanation:
We have the two functions: [tex]f(x)=2x-3[/tex] and [tex]g(x)=x^2[/tex].
14)
We want to find x if [tex]f(x)=3[/tex].
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, [tex]2x-3[/tex], for f(x) and solve for x. This gives us:
[tex]2x-3=3[/tex]
Solve for x. Add 3 to both sides:
[tex]2x=6[/tex]
Divide by 2:
[tex]x=3[/tex]
So, [tex]f(3)=3[/tex], and our x is 3.
16)
We have: [tex](g\circ f)(2)[/tex]
This is known as composition of functions. This is equivalent to [tex]g(f(2))[/tex]
So, let's find f(2) first. We know that:
[tex]f(x)=2x-3[/tex]
Substitute 2 for x:
[tex]f(2)=2(2)-3[/tex]
Evaluate:
[tex]f(2)=4-3=1[/tex]
Therefore, our composition of functions can be rewritten as:
[tex]g(f(2))=g(1)[/tex]
Find g(1). We know that:
[tex]g(x)=x^2[/tex]
Substitute 1 for x:
[tex]g(1)=(1)^2[/tex]
Evaluate:
[tex]g(1)=1[/tex]
Therefore:
[tex](g\circ f)(2)=1[/tex]
