Question

Express your answer as a polynomial in standard form.

Answer:
f(x) = 5x - 4
g(x)=x²-3x - 11
Find: (fog)(x)
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Answer 1

To find (fog)(x), we need to first find g(x) and substitute it into f(x).

g(x) = x² - 3x - 11

Now, we substitute g(x) into f(x):

f(g(x)) = 5g(x) - 4

= 5(x² - 3x - 11) - 4 (substituting g(x) into f(x))

= 5x² - 15x - 55 - 4

= 5x² - 15x - 59

Therefore, (fog)(x) = 5x² - 15x - 59.

Answer 2

(f o g)(x) =

5x²-15x - 51

Explanation:

(f o g)(x) means to wad up g(x) and stuff it into the place of x in f(x).

(f o g)(x)

means f( g(x) )

Here's f(x)

f(x) = 5x - 4

If you were calculating f(2) you would put a 2 in place of x. Or f(18) you would put 18 in place of the x. In this case we will cram the entirety of

x²-3x - 11 into the place of x.

f(x) = 5x + 4

Let's make a lot of room for g(x).

f(x) = 5___x_____ + 4

Okay, here we go:

f(g(x))

= 5(x²-3x - 11) + 4

See how we replace the x in f(x) with the whole entire g(x).

Now we'll simplify because they asked for standard form.



f(g(x))

= 5(x²-3x - 11) + 4

Use distributive property.

= 5x²-15x - 55 + 4

Combine like terms.

= 5x²-15x - 51

(f o g)(x) =

f( g(x) ) = 5x²-15x - 51