[tex]\boxed{A. \ f(g(2)) = -7 \ }[/tex]
In this problem we will find out the value of the function composition. There are two ways to do it.
[tex]\boxed{ \ f(x) = x + 8 \ }[/tex]
[tex]\boxed{ \ g(x) = x^2 - 6x - 7 \ }[/tex]
[tex]\boxed{ \ f(g(2)) = ? \ }[/tex]
First way
Step-1: compose (f o g)(x) = f(g(x))
Here g(x) as input into f(x). In other words, first we apply g(x), then apply f(x) to that result:
[tex]g(x) = x^2 - 6x - 7 \rightarrow f(x) = x+8[/tex]
[tex]f(g(x)) = (x^2 - 6x - 7) + 8[/tex]
[tex]f(g(x)) = x^2 - 6x - 7 + 8[/tex]
And we get,
[tex]\boxed{ \ f(g(x)) = x^2 - 6x + 1 \ }[/tex]
Step-2: calculate the value of f(g(2))
After getting f(g(x)) we proceed by calculating the value f (g(2)).
[tex]x = 2 \rightarrow f(g(2)) = (2)^2 - 6(2) + 1[/tex]
[tex] f(g(2)) = 4 - 12 + 1[/tex]
And we obtain the final result:
[tex]\boxed{ \ f(g(2)) = -7 \ }[/tex]
Second way
Step-1: count g(2) initially
[tex]x = 2 \rightarrow g(2) = (2)^2 - 6(2) - 7[/tex]
[tex] g(2) = 4 - 12 - 7 [/tex]
And we get,
[tex]\boxed{ \ g(2) = -15 \ }[/tex]
Step-2: calculate the value of f(g(2))
Here the value of g(2), i.e. -15, as input into f(x).
[tex]g(2) = -15 \rightarrow f(-15) = -15 + 8[/tex]
And we obtain the final result:
[tex]\boxed{ \ f(g(2)) = -7 \ }[/tex]
Keywords: Let f(x) = x + 8 and g(x) = x² - 6x - 7, find f(g(2)), composition function, input, f(g(x)), value, initially,
Answer:
Option A.
Step-by-step explanation:
The given functions are f(x) = x + 8 and g(x) = x² - 6x - 7
We have to find f[g(2)].
To find f[g(2)] we have to find f[g(x)] first.
f[g(x)] = (x² - 6x - 7) + 8 { we will replace x by the g(x) in the function f(x)]
f[g(x)] = x² - 6x + 1
Now f{g(2)] = 2² - 6(2) + 1
= 4 - 12 + 1
= 5 - 12
= -7
Therefore, f[g(2)] = -7 will be the answer.
Option A is the correct option.
