Answer:
(g o f)(-5)= 9
Step-by-step explanation:
Given : [tex]f(x) = x+2[/tex]
[tex]g(x)=x^{2}[/tex]
To Find : (g o f )(-5)
Solution :
We are supposed to find the value of (g o f )(-5)
So, first understand that (g o f )(x) means g(f(x))
Now putting value of x :
(g o f )(x) =g(f(x))
⇒(g o f)(-5)= g(f(-5)) --(a)
Now for solving further we need to find value of f(-5)
Since we are given that [tex]f(x) = x+2[/tex]
⇒ [tex]f(-5) = -5+2[/tex]
⇒ [tex]f(-5) = -3[/tex]
Now put this value in (a)
⇒(g o f)(-5)= g(-3) ----(b)
Now we need to calculate the value of g(-3)
Since we are given that
[tex]g(x)=x^{2}[/tex]
⇒[tex]g(-3)=(-3)^{2}[/tex]
⇒[tex]g(-3)=9[/tex]
now put this value in (b)
⇒(g o f)(-5)= 9
Hence , (g o f)(-5)= 9
