Given f(x) =x-7 and g(x)= x^2 find f(g(-1))

-6

Step-by-step explanation:

f(g(-1)) means we need to find g(-1) and then plug that result into f(x).

So let's start:

g(-1) means to replace the input variable in g(x)=x^2 with -1.

So we replace x with -1.  

g(-1)=(-1)^2

g(-1)=1

Now that we have g(-1) can be replaced with 1, we can further evaluate f(g(-1)).

So let's do that:

f(g(-1))

f(1)=1-7   ; I replaced the x in f(x)=x-7 with 1 to find f(1).

f(1)=-6

Putting altogether

f(g(-1))=f((-1)^2)=f(1)=1-7=-6.

f(g(-1)) = -6

Step-by-step explanation:

* Lets explain how to solve the problem

- The problem is about the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted into

 another function.

- Ex: f(g(x)) is the composite function that is formed when g(x) is

 substituted for x in f(x)

* lets solve the problem

∵ f(x) = x - 7

∵ g(x) = x²

- We want to find f(g(-1))

* At first lets find g(-1) by substitute x in the function g(x) by -1

∵ g(x) = x²

∵ x = -1

∴ g(-1) = (-1)² = 1

* Now we want to find f(g(-1)), then we will substitute x in f(x) by

 the value of g(-1)

∵ g(-1) = 1

∵ f(x) = x - 7

∴ f(g(-1)) = f(1)

∵ f(1) = 1 - 7 = -6

∴ f(g(-1)) = -6

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

c

step-by-step explanation: