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If f(x)=4x^2 and g(x)=x+1, find (fog)(x)

iren [92.7K]

Answer: The value of $(f_\circ g)(x)$ is $4(x+1)^2$ .

Step-by-step explanation:

Given: $f(x) = 4x^2 \text { and } g(x) = x+1$

To find: $(f_\circ g)(x)$

As we know it is composition function which means that g(x) function is in f(x) function.

So we have

$(f_\circ g) (x) = f[g(x)]$

$\Rightarrow( f_\circ g)(x)= f(g(x)) = 4(g(x))^2$

Now substitute the value of g(x) we get

$(f_\circ g)(x)= 4(x+1)^2$

Hence, the value of $(f_\circ g)(x)$ is $4(x+1)^2$ .

5 0

3 years ago

PLEASE!!! NEED HELP ASAP!!! 50 PTS AND BRAINLIEST!!!

noname [10]

1) Inverse function: $f^{-1}(x)=g(x)=\frac{x+4}{3}$

2) $f(1) = -1, g(-1) = 1$

3) $f(g(x))=g(f(x))=x$

Step-by-step explanation:

1)

In this first method, we want to find the inverse function of $f(x)$ .

The original function is:

$f(x) = 3x-4$

We rewrite it as

$y=3x-4$

We swap the name of the variables:

$x=3y-4$

Adding +4 on both sides:

$x+4=3y-4+4\\x+4=3y$

And dividing by 3 on both sides:

$y=\frac{x+4}{3}$

which is identical to $g(x)$ :

$g(x)=\frac{x+4}{3}$

2)

In this second method, we want to use the output of one function as input to the other function, and show that the output value is equal to the imput value.

We start using the function

$f(x)=3x-4$

We choose $x=1$ . We find:

$f(1)=3(1)-4=3-4=-1$

Now we use this output value as input in the function

$g(x)=\frac{x+4}{3}$

Substituting $x=-1$ ,

$g(-1)=\frac{-1+4}{3}=\frac{3}{3}=1$

So, the final output value (1) is equal to the input value (1).

3)

Here we want to verify that the two are inverse functions by showing that

$f(g(x))=x$

We have

$f(x)=3x-4\\g(x)=\frac{x+4}{3}$

Substituting g(x) into f(x),

$f(g(x))=3g(x)-4 = 3(\frac{x+4}{3})-4=(x+4)-4=x$

Viceversa, we want to show that

$g(f(x))=x$

Substituting g(x) into f(x), we get

$g(f(x))=\frac{f(x)+4}{3}=\frac{(3x-4)+4}{3}=\frac{3x-4+4}{3}=\frac{3x}{3}=x$

So, the two functions are one the inverse of the other.

Learn more about inverse functions:

brainly.com/question/1632445

brainly.com/question/2456302

brainly.com/question/3225044

#LearnwithBrainly

6 0

3 years ago

Ideas for an one-act play?

AURORKA [14]

Answer:

what is that

Step-by-step explanation:

roeeo

6 0

3 years ago

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There are 52 playing cards in a standard deck of cards. If Patrica selects a card at random, what is the probability that it wil

Alisiya [41]

Since there are two black queens out of 52 cards, there is a 2/52 chance of drawing a black queen first. This is equivalent to a 1/26 chance.

Now that we have removed a black queen, there are 51 cards left in the deck. 26 of them are red because we only took away a black card. This means that there is a 26/51 of drawing a red card next.

In order to find the probability of both of these happening, we multiply the two together. 1/26 * 26/51 = 26/1326. This reduces to 1/51. So, there is a 1/51 chance of drawing a black queen, then a red card.

8 0

3 years ago

Solve each equation:

timurjin [86]

1.) x=-9 because
2.) x=16

3 0

3 years ago

Read 2 more answers