Given that f(x) = 3x + 4 and g(x) = x2, find the following.?

Question

1. 2f(5)

2. f(2) * g(2)


I'm not exactlly sure where to start
Please explain the whole process so I may understand how to solve future problems
Thank you for the help in advance

Answer 1

Find the following when f(x) = 3x + 4 & g(x) = x^2

1. 2f(5)

First: replace "5" with the "x" variable in the f(x) function....

f(x) = 3x + 4

2f(5) = 2(3*5 + 4)

2f(5) = 2(15 + 4)

2f(5) = 2(19)

2f(5) = 38

2. f(2) * g(2)

First: replace "2" with the x-variable in the f(x) function 7 replace "2" with the g(x) function.....

(3x + 4)(x^2)

(3*2 + 4)(2^2)

(6 + 4)(2*2)

(10)(4)

40

Answer 2

f(x) or g(x) or y(x) or z(x) are called functions. This means, when you plug in a number or value in for x, the function will spit out another value. Think of it as a machine, this machine is called f(x). For whatever value "x" you put into the machine, f(x) will spit out something related to that x. Lets go through an example. We have a f(x) machine that will always double your input. Well how do you describe this machine in words? f(x)=2x. That means, for whatever x value you put in, f(x) will always be 2 times that value. If you put in 2 for x, f(2)=2(2) so f(2) equals 4.

So for your problem, you have a f(x)=3x+4 and a g(x)=2x. Thus, you have essentially 2 machines, the f(x) and the g(x). Lets use the machine analogy again and tackle the first part. 2f(5)=what? Well, what is this really asking? First you have to decide which machine this problem is talking about. 2f(5) wants you to pick out the f(x) machine rather than the g(x) machine. 2f(5) states that the "x" value for this machine will have to be 5. Thus, when you put a value of 5 into the f(x) machine, you get f(x)=3x+4, 3(5)+4, which equals 19. Thus, f(5) equals 19. However, they want 2 times f(5) so 2 times 19 is 38.

Hopefully that makes sense.

We do the same thing for the second part. f(2) refers to the f(x) machine. 3(2)+4 equals 10. g(2) refers to the g(x) machine. 2(2) equals 4. Then just use simple multiplication. 10 times 4 equals 40.

There you go, your answers are 38 and 40.

Answer 3

Question 1.
f(5) = 3 x 5 + 4 = 19
2f(5) = 2 x 19 = 38

Question 2
f(2) = 3 x 2 + 4 = 10
g(2) = 2² = 4
f(2) . g(2) = 10 x 4 = 40

Answer 4

1. 2f(5). When you have a problem such as f(5), you put the number in the parenthesis into the x in the problem. So f(5) would be f(5)=3(5)+4. This equals 19. The two in front of the problems simply means you multiply this value by two. The correct answer is 38. For the next problem, you have two seperate problems to work out first. f(2)=3(2)+4. f(2)=10. g(2)=(2)*2. g(2)=4. f(2)*g(2)=10*4= 40. It's pretty simply once you understand what f(x) means.

Answer 5

OK. like all functions equations you start in the middle.
The first problem means that f(5) and multiple all of that by 2
2f(5)= 2[3(5)+4]
2f(5)= 2[15+4]
2f(5)=2(19)
2f(5)=38
Now, try the second problem! I'll get you started(I assume that by putting *, you mean multiple)
[3(2)+4]*[2(2)]

Answer 6

1. Given that f(x) = 3x + 4, a statement such as f(4), f(3), f(2) 2*f(2) means replace 'x' in f(x) with the number inside the parentheses.

So f(5) means x = 5
f(5) = 3*5+4
f(5) = 19

Any operation done outside i.e. (f(x) * g(x))
1. Evaluate the function 'f(x)' at x
2. Evaluate the function 'g(x)' at x
3. Take the product of these two answers.

Likewise 2*f(6) means evaluate f(6) first, then multiply that answer by two.

f(6) = 22
2*f(6) = 2*22=44

Another possibility is to nest the functions
f(g(x))

As you would expect, evaluate g(x) first, then use that answer to evaluate f(x)

f(g(x)) may also be written as
p = g(x)
f(p)

Answer 7

for number 1 plug in 5 into the function and solve. then multiply by 2
for number 2 plug in 2 for both functions. and multiply their answers together


1. 3(5) + 4 = 19 x 2 = 38

2. (fg)(2) = 10 x 4 = 40

Answer 8

1.2f(5)
First we find f(5) first. Whenever you see x you can replace be 5
So f(5)=3*5+4=15+4=19
2f(5)=2*19=38
2. g(x)=x^2
Find f(2) you can replace x by 2
F(2)=3*2+4=10
G(2)=(2)^2=4
F(2)*g(2)=10*4=40
Good luck.

Answer 9

you could exchange (3x + 4) into y and so which you would be waiting to comprehend the calculation extremely. (2x + 5)(3x + 4) = (2x + 5)y = 2x(y) + 5(y) = 2x(3x + 4) + 5(3x + 4) (answer c)

Answer 10

ok you just plug in everything.
so for number one, plug F in.
SO.... 2 (3x+4) (5)

and 2. is
(3x+4) (2) * (x2)(2)