Question

Let f(x) = x2 - 4x and g(x) = 2x – 3. Find f(g(4))

Answer 1

Answer:

$f(g(4)) = 5$

Step-by-step explanation:

f(x) = x² - 4x

g(x) = 2x – 3

To find f(g(4)) we must first find f(g(x))

To find f(g(x)) substitute g(x) into f(x) that's for every x in f(x) replace it with g (x)

That's

$f(g(x)) = ({2x - 3})^{2} - 4(2x - 3) \\ = 4x^{2} - 12x + 9 - 8x + 12 \\ = 4 {x}^{2} - 12x - 8x + 9 + 12$

We have

$f(g(x)) = {4x}^{2} - 20x + 21$

Now to find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4

We have

$f(g(4)) = 4( {4})^{2} - 20(4) + 21 \\ = 4(16) - 80 + 21 \\ = 64 - 80 + 21 \\ = 85 - 80$

We have the final answer as

$f(g(4)) = 5$

Hope this helps you

Answer 2

Answer:

Answer:

f(g(4)) = 5f(g(4))=5

Step-by-step explanation:

f(x) = x² - 4x

g(x) = 2x – 3

To find f(g(4)) we must first find f(g(x))

To find f(g(x)) substitute g(x) into f(x) that's for every x in f(x) replace it with g (x)

That's

\begin{lgathered}f(g(x)) = ({2x - 3})^{2} - 4(2x - 3) \\ = 4x^{2} - 12x + 9 - 8x + 12 \\ = 4 {x}^{2} - 12x - 8x + 9 + 12\end{lgathered}

f(g(x))=(2x−3)

2

−4(2x−3)

=4x

2

−12x+9−8x+12

=4x

2

−12x−8x+9+12

We have

f(g(x)) = {4x}^{2} - 20x + 21f(g(x))=4x

2

−20x+21

Now to find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4

We have

\begin{lgathered}f(g(4)) = 4( {4})^{2} - 20(4) + 21 \\ = 4(16) - 80 + 21 \\ = 64 - 80 + 21 \\ = 85 - 80\end{lgathered}

f(g(4))=4(4)

2

−20(4)+21

=4(16)−80+21

=64−80+21

=85−80

We have the final answer as

f(g(4)) = 5f(g(4))=5

Hope this helps you