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ollegr [7]
3 years ago
8

If f(x) = 3x– 2 and g(x) = x^2– 5, what is g(f(2))?

Mathematics
1 answer:
Lunna [17]3 years ago
7 0

Answer:

\large\boxed{g\bigg(f(2)\bigg)=11}

Step-by-step explanation:

f(x)=3x-2,\ g(x)=x^2-5\\\\g\bigg(f(2)\bigg)=?\\\\\bold{STEP\ 1:}\\\text{Calculate}\ f(2).\\\text{Substitute}\ x=2\ \text{to}\ f(x):\\\\f(2)=3(2)-2=6-2=4\\\\\bold{STEP\ 2:}\\\text{Substitue}\ x=4\ \text{to}\ g(x):\\\\g(4)=4^2-5=16-5=11

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Find the sum of the first 20 terms of the arithmetic sequence 4, 10, 16, 22....
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n = 20

d = 6

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How to solve using substitution<br> y=3/4X+5<br> 4x-3y=-1
Pachacha [2.7K]
Please, use parentheses to enclose each fraction:
y=3/4X+5 should be written as <span>y=(3/4)X+5

Let's eliminate the fraction 3/4 by multiplying the above equation through by 4:

4[y] = 4[(3/4)x + 5]
Then 4y = 3x + 20
(no fraction here)

Let 's now solve the system   

4y=3x + 20
4x-3y=-1

We are to solve this system using subtraction.  To accomplish this, multiply the first equation by 3 and the second equation by 4.  Here's what happens:

12y = 9x + 60  (first equation)
16x-12y = -4, or -12y = -4 - 16x (second equation)

Then we have 

 12y = 9x + 60
-12y =-16x - 4

If we add here, 12y-12y becomes zero and we then have 0 = -7x + 56.
Solving this for x:  7x = 56; x=8

We were given equations   
</span><span>y=3/4X+5
4x-3y=-1

We can subst. x=8 into either of these eqn's to find y.  Let's try the first one:

y = (3/4)(8)+5 = 6+5=11

Then x=8 and y=11.

You should check this result.  Subst. x=8 and y=11 into the second given equation.  Is this equation now true?</span>
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