Question

Let f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2)).

Answer 1

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.

Answer 2

$\boxed{A. \ f(g(2)) = -7 \ }$

Further explanation

In this problem we will find out the value of the function composition. There are two ways to do it.

$\boxed{ \ f(x) = x + 8 \ }$

$\boxed{ \ g(x) = x^2 - 6x - 7 \ }$

$\boxed{ \ f(g(2)) = ? \ }$

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:

$g(x) = x^2 - 6x - 7 \rightarrow f(x) = x+8$

$f(g(x)) = (x^2 - 6x - 7) + 8$

$f(g(x)) = x^2 - 6x - 7 + 8$

And we get,

$\boxed{ \ f(g(x)) = x^2 - 6x + 1 \ }$

Step-2: calculate the value of f(g(2))

After getting f(g(x)) we proceed by calculating the value f (g(2)).

$x = 2 \rightarrow f(g(2)) = (2)^2 - 6(2) + 1$

$f(g(2)) = 4 - 12 + 1$

And we obtain the final result:

$\boxed{ \ f(g(2)) = -7 \ }$

Second way

Step-1: count g(2) initially

$x = 2 \rightarrow g(2) = (2)^2 - 6(2) - 7$

$g(2) = 4 - 12 - 7$

And we get,

$\boxed{ \ g(2) = -15 \ }$

Step-2: calculate the value of f(g(2))

Here the value of g(2), i.e. -15, as input into f(x).

$g(2) = -15 \rightarrow f(-15) = -15 + 8$

And we obtain the final result:

$\boxed{ \ f(g(2)) = -7 \ }$

Learn more

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Keywords: Let f(x) = x + 8 and g(x) = x² - 6x - 7, find f(g(2)), composition function, input, f(g(x)), value, initially,