Answer:
F(G(2))=23
Step-by-step explanation:
To solve this problem we need to find the equation from each line, then find the expression for the composite function F(G(X)) and finally evaluate it in x=2.
The given functions behave like lines, hence we will use an approach of the same matter.
F(x)=ax+b where, 'a' is the slope and b the interception with 'y'=axis
G(x)=cx+d where, 'c' is the slope and d the interception with 'y'=axis
Using the first point (x=0) we will obtain 'b' and 'd'.
F(0)=a*0+b=5, we have b=5
G(0)=c*0+d=3, we have d=3
To obtain the slope of every function we need to use the equation for slopes
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where (x1,y1)=(0,5) and (x2,y2)=(1,7) for F(x) and (x1,y1)=(0,3) and (x2,y2)=(1,6) for G(x)
Using the above equation, we have that a= 2 and c=3
Hence
F(x)= 2x+5
G(x)=3x+3
Now the composite function is obtained by replacing 'x' inside F(x) by G(x)
F(G(x))=6x+6+5
Evaluating in x=2
F(G(2))=6*2+11=23
